professor or min 19 27 and was in a lonely over superior Kishan and the University door say he took in 1985 a reserve position at coloma super jerko les de france since nineteen nineteen ninety-two he has been SN arises senior researcher at the Institute optic a is now professor at the destitute of trick graduate school share August infernal and a tad ecole polytechnique in a Palazzo is the member of many Academy cerca de limitations marie-france lock at a media technology francaise la national academy of sciences USA the restaurant Academy from vision Shafton Ostia académie royale the basic and Royal Society he got many many awards received many awards the sierras gold medal 2005 duvall prize in physics 2010 to Mazzoni award 2013 the balthon price on quantum information 2013 the needs boar gold medal 2013 and the Albert Einstein medal 2013 on his research professor Hinkle fuel will give more information I just want to welcome professor respect in our Academy and also tell you that I got a letter from the foundation occasionally balthon where the president’s professor the clava and president of the committee of the prize committee professor Salvatore a vaca say that they are very happy that we invited here professor a spectacle he was a recipient of the balsam prize in 2013’s they said and they apologize for not being able to attend his lecture so welcome professor layton our Academy and I give you now world to Professor Marco Jilly rector Adele politécnica de Turini yes good morning Thank You Alberto it’s a pleasure to be here and also to welcome all of you here for this very exciting and very interesting lecture of a vessel aspect well there are many reasons why the Politecnico di torino easier of course the first reason is that we are going to a word Galilee of rallies price and you know that yellow ferraris was a professor in the politecnico di Torino at that time I was not yet named politécnica de torino it was there a girl in dust museum but Jennifer Harris was the first professor of electrical engineering we still have the name a little techniques which is not in English but there was the first professor of electrical engineering he also founded the associations of Italian electrical engineers and and of course it was one of the most brilliant scientists in addition to some others that have been hearing this Academy like Lagrange it was one of the most brilliant scientists of this region there is a second reason of course we are very happy to be here and is that this is the international year of the light and you know more and more in technical university we realize that now I to say the principles of quantum physics are coming into technology and we have a lot of activity regarding photonics but if you think to hold the disruptive technologies that will have a great impact both economical and social impact so you you find that photonics additive manufacturing and so so require now in a way to merge together fundamental physics and and technology man this is a real challenge

for for the future I’m sure that in the future more and more of our activity in technical university will concerns quantum science and quantum technology so that’s why you know there’s another reason you know we are very happy to be here and finally the third reason is that since many many years since the time in which the interim Institute was split it in two parts one part was colonnaded the other party no was entitled to Galileo fellas there is being a very strong collaboration between our departments in the Polytechnic a little you know and the department and the sections of the Galilee of arrives Institute there are some schools of the politecnico di Torino like the school of electronics and the School of Computer Engineering that were founded exactly by professors that were researchers in the gallery of agave so there’s been the very very strong connection between him and the politecnico di Torino and in the future we think that this connection could be strengthened just by focusing on some subject that related to in some way to the lecture professor aspect and to the field of quantum science and quantum technology so it’s really a pleasure to welcome here into tank of a suspect for for coming here for honoring us with his presence here in this Academy and in this city and I thank you for your attention visto che abbiamo celebrate okok a genova the necessary dante alighieri window radio of Witter so Rocco tanto say no I’d like to to take the opportunity of one of the last the statements of the rector Marco Chile to say that essentially with the gorilla Ferraris you implement and wean Italy had a qualitatively magic moment that was the moment when something which was a up abstract a sort of conceptual story like the Maxwell equations they turned out to be to become technology with the story of a production of late electricity from from a very nice equation that now the reason why today we are eager to to give this price to Professor Alan a spare ooh since now we will call Alan will be maybe explain later but essentially it is because there has been one of the others many major via magic moments in in physics and this happened in around nineteen eighty one two amino three where quantum mechanics was still a a conceptual debate was was a philosophy was probably was the most important philosophical revolution of of the last century and the debate I see a specialist so I don’t want to enter this field but the bait was whether it was possibility to have eaten variables that under non-separable ax t of the variable I’m using you know technical they taking and stuff essentially you know that and I think that Alan will explain this there was all the debate on on the DDT the completeness or no of the quantum mechanics but sometimes the revolutions comes as a consequence of surprises so I was a student in Pisa when my my professor would see you know we did the history essentially asked us young people to come and talk a little bit with this young guy coming from from Paris making the PhD on his own idea

which was a totally strange idea so total totally new and the idea was to put together an experiment to to see whether it was possible to transform a Gedanken experiment into a real experiment and this was made possible by any and inequality that ballad written a mean and so on so first of all that is a demonstration our young people when they are brave or few of them are brave they are able to you know to go in a new direction I think it not much support in in general in the in the French everywhere i’m in a classical I mean environment then he made really this experiment and immediately and imagine that they will talk about this it may immediately essentially made possible the realization later on of the far-seeing idea of Richard Feynman 10 in 82 with a lot with a huge fantasy yet written about the possibility of putting together a quantum computer or a quantum simulator and so on now a quantum computer is possible or maybe really possible because of the entanglement and which is this strange world and tangling that in franchising and intricacy on and in Italy you know we don’t translate because the French did to translate everything computer internet entanglement intricacy on so the demonstrated the possibility with is experiment of this revolutionary think of the intricacy on Quantic the which now makes possible the essential of the quantum technologies and the in particular the quantou metrology tomorrow we are going together to a special round table which is in in Brussels where the idea is to show that now really more and more precise measurement and test and tactile technology can be can be done according to the surprise that he produces for all the world that really dead crazy experiment or having two photons leaving an atom of calcium going one left and the other one right they still remember essentially each other was there was a correlation between the two so this was essentially this is a revolution making possible is the key story this is the reason why I got to the bottom price make impossible what Marco Jilly was saying that now quantum mechanics is becoming a real technology pay attention not the technology like the laser one because the laser is of course is a consequence of a quantum mechanics or even the transistor but there we are using the laws of quantum mechanics to create a tool here the quantum mechanic itself is becoming I mean a technology Alan has written many books and but also together with a few Nobel prizes is his quarter of overbooking French the mainland ashiq so what will be the physics the man and I think that is a no one the world is as good as a Zima in talking what could be in the future because this book is full of ideas again which assure the progress of science for a meaningful for diffusion then I would lie then my president has already made the long list of prizes he has got all the prizes so but one who knows and even Italy is a water demon internet important international price university of rome as an international price or may say that Italy’s is recognized emma is a green scientist but let me conclude telling why we told that this price had to be offered to him in this in this Academy I mean one of the many lectures that has been given in the past this has been in berlin in the in the village little villa of the the german physical society where lagrange which which was the outs of lagrange and this talk was given in the frame of something

organized between italy germany and france in honor of lagrange so i assisted to a wonderful talk oberlin the French invited by the Germans in the house of LaGrange with myself as the Italian making the you know the introduction and the comments so I think that it’s absolutely necessary to have this this award to given to a LAN I mean in the in this place because really you know we are talking of revolutionary ideas in in this sort of i mean a European European scale so this is what I wanted to add to what already the president and director is f saved and so probably at this point I think that Elena you could you could start or I give the ball to the president say well thank you for registering Gushue Thank You professor chile very glad and happy and proud to introduce to Professor Lang aspect who we speak for his lecture magistratus on the topic from the Einstein board abated to bells inequalities tests precision measurement settle a conceptual debate okay yes so I think that what is interesting in the in the story I’m going to tell you a that really it’s a story that goes from concept to technology from conceptual debate to precise measurements and I think it cover all the different side of the of signs the most conceptual the most technological and precision so I like to have a subtitle which is from the Einstein body bae to quantum technologies are we leaving a new quantum revolution and I have a prejudice that yes we are leaving a new quantum revolution so let us start with the MM emergence of quantum technologies and more particularly quantum information if you google quantum informations you have hundreds of millions of results and I have selected a few of them there is a journal on quantum information the New York Times speaks about quantum information I am sure that Italian newspaper also speak of quantum information not French newspaper French newspaper are not interested in science but I think that you are more civilized that than we are there is an Institute for quantum information in Cal Tech in MIT in cambridge UK so really it seems to be an important day but how did it emerge well i think here we have the main actors Einstein and Bohr the big debate between Einstein and Bohr I will explain more in detail in a while reading her who added is grain of salt exactly at the same moment in 1935 Schrodinger was certainly among his big people was certainly the one who immediately understood the importance of the debate between Einstein and Bohr and then John Bell Oh 30 years later that is to say in 65 totally renewed the debate and what did they find they find that entanglement is different different from what different from what usually we think of the strangeness of quantum mechanics when you think of the strangeness of quantum mechanics you think of wave-particle duality no doubt this is strange but what these people realized if that entanglement is different and it took a long time to be recognized believe it or not when I started my PhD as a Massimo evoked so in 74 75 most of the people will tell you look Alan what what you want to demonstrate we know already it’s waste particle duality and I say no no no entanglement is not the same thing it took a long time to rate to be realized and these people are people realized it and then fine man you mention it in 82 Fineman recognized that entanglement is different because if you read lectures on physics he say all the mystery in quantum mechanics is in wave particle duality

20 years laters after lecture on physique you see are there isn’t in you entanglement but fine and being fine and as soon as he recognizes that there is something new he invents a way of applying it and it was the invention of the concept of quantum computation so entanglement not only is different but it is more ok so now I will will be the main part of my talk I will talk about the unch line board debate bells inequality test and here are some references this is a wonderful book with the text of John Bell about the concepts of quantum and the conceptual debates of quantum mechanics is a wonderful book this is a book by nicholas reason which I think it’s a quite good book about the the foundation of quantum mechanics it puts the emphasis on the dramatic character of randomness in in quantum physics and I think that is fully right so right so these weights called quantum chance there is also a lot of quantum nonlocality and these text book on quantum optics I am one of the authors so if you buy it for your library I get some royalties you know i can i can pay for one or two cups of coffees no it’s good but the important thing is that in this book you have all the calculations which allow you to get the result i will cite here if you don’t want to pay for the book you can go to my home page and you can download these calculations for free okay so make your choice okay and shine einstein and quantum physics i’m sure you know that Einstein is really one of the founders of quantum mechanics we should not forget that of course we know of plonk 1900 but in night from 1900 was desperate and this is why he called this constant h42 he refer help you know it was desperate and he did not like at all the hypothesis made that exchanges of energy between radiation and matter are quantized okay but it is not like that at all Einstein in 1905 made a strong hypothesis that radiation itself is quantized not only the exchanges radiation itself so we should consider really I’m Stein a major founding father of quantum mechanics okay and remember that he got the Nobel Prize for his hypothesis that radiation is made of leashed kwanten okay as he said we did not use the word photon is a cuanto flight least kwanten in this year’s of light it appropriate to remember it but you know what happened Undine was more and more dissatisfied in the way quantum mechanics was developed and more precisely in the philosophy of the people we’re developing quantum mechanics also called Copenhagen school okay it was really not happy he had no problem with the mathematical calculations it was a nappy with the interpretation and he came with plenty of objections precisely about wave particle duality plenty of objections about the Heisenberg so-called uncertainty relation and for this I must say that Nils go could always reply to one Stein and show that Einsteins objections did not stand the Copenhagen interpretation was really consistent to describe wave particle duality and eisenberg uncertainty relation and then in 1935 Einstein came with totally different objections it’s a famous Einstein Podolsky Rosen program that i will describe now this objection was underestimated a long time until Bell and this n entanglement is now at the core of quantum information and of a part of quantum etiology so what is equation that Einstein was asking in 1935 which is collect boris podolsky nothin rose and the problem is the question is a following you all know that in most situation when you do calculation of quantum mechanics you get a probabilistic result the probability to find the spin on the up dot is 40-person the probability to find it down is sixty percent etc and so on china was asking the equation is it possible to explain the probabilistic nature character of

quantum prediction by invoking a supplementary underlying level of description what does mean think of the maxwell-boltzmann distribution of the velocities of the molecules flying here in the atmosphere okay we have no problem for new conceptual problem because we think that it is convenient to use a Maxwell Boltzmann distribution but we have no doubt that each particular molecule has a well-defined velocity and it’s just a convenience to describe it by law of probability so understand as equation isn’t it the case that the statistical nature of the prediction of quantum mechanics tells us that there is an underlying description more precise where each object would have a precise behavior and it is convenient to us that kind of statistical theory and Einstein thought that with reasoning I am going to describe now he had found a positive answer to this equation and we will see that ball immediately was strongly opposed so let us describe an Einstein Podolsky Rosen Gedanken experiment at that time it was really an ideal experiment and it’s not exactly the scheme that Einstein was describing at that time I prefer to describe immediately in the modern form with photons because it is this form which has been realized in real experiments so what do we have web source emitting two photons a photon to the left foot onto the right I show them with different colors to avoid the confusion that the problem stems from the NDC an ability here they are perfectly discernible this one as a coder this one another one you put a filter here today you know which photon is which so no question of indecent ability now on this photon you make a measurement of polarization so you can think that this is a birefringence p crystal or for a stone prisma whatever what does it means it means that you have an optical axis here and if the polarization is parallel to the axis the photon will be found in the plus 1 channel and if the polarization of the photon is orthogonal to the direction of the axis you will find it in the minus 1 channel and now of course the equation which immediately takes us to the probabilistic character of quantum mechanics if you have a beam of light a macroscopic beam of light and if the polarization is at an angle of these axes a fraction of the beam will go up and a fraction of the beam will go down and it’s a male slow etc but if you have a single photon the photon cannot be cut into ok so if the photon has a polarization which is neither parallel nor perpendicular to the axis of the polarizer there is a certain probability to find the photon up and a certain probability to find the photon down so we can define probabilities P plus a which means probability to find the photon in the channel plus one when the orientations a etc more interesting is to consider the joint probability that the first photon is found here and the second photon is from there I should have said that I have another polarizer in orientation be for the second photo ok so the joint probability P plus plus of a B is a probability to find plus one here and plus one here when the orientation are a and B ok and I have this for probability at this point is just an experiment we can think of it there is no ensign Podolsky Rosen yet now comes and Stein Podolsky Rosen the discovery of Einstein Podolsky and Rosen is that the standard formalism of quantum mechanics just using the basic principle of quantum mechanics as explained for instance in the book of Dirac ok at that time the book did exist already the formalism of quantum mechanics allows you to consider that state what is this take let us spend one minute on it here you have the access when I here I describe only the polarization part of the wave function describing the two photo ok I don’t describe the propagation etc etc ok I just concentrate on the polarization part x correspond to the first photon polarized along the axis X the second X here correspond to the photo new to authorised around X so X X describes a pair of photons authorized vertically YY describes a pair of photon polarized horizontally what Einstein Podolsky and

Rosen say look at the basic principle of quantum mechanics we are allowed to consider a state like that which is a superposition of vertical vertical plus horizontal horizontal and they say this is really very strange because don’t make any confusion this does not mean that you have a pair of photon with the polarization at 45 degrees no no you cannot you cannot factorize this state as a product of state describing the first photon times stay describing the second one mathematician have no problem to show that this cannot be factorized you are in space which is a tensor product and it is well know that in the tensor product state most of the vectors cannot be factorized ok now starting from this it is quite easy to calculate the probabilities of the various results here so we assume that we can produce a pair of photons like that what are the prediction of quantum mechanics so at this point you go to my book or you go to what you load on my homepage is not very difficult I would say its third or fourth year of University okay what do you get first single probabilities P plus P minus equal one of whatever the orientation that is to say these photons appears as totally and polarized whatever you do you get fifty percent chance to get plus fifty percent chance to get minus and whatever the orientation same on the other side for the second photo now when you look at the joint detection now you have interesting formulae as a function of the orientation of the two polarizer it depends on the angle between the two polarizer ap is the angle between the two orientations and so let us focus on the special case where this polarizer and this polarizer are parallel that is to say the angle is zero when you look at this formula you find P plus price equals P minus minus equals one-half and P plus minus equal P minus plus equals zero this does not look interesting but it is very interesting it is very interesting because it tells you that the results of the measurement are totally authorized totally correlated excuse me why do I say that one ass doesn’t look too toric already yes remember that the probability that the first photon gives plus is one off and now the joint probability is also one of which means that the conditional probability is a hundred percent in other words these photon arrives here there is fifty percent chance to find it here fifty percent chance to find it there but if you find the first photon here you are sure to find the second photo non plus one and if you find this one on minus one you are sure to find the other one on minus one and if you are not yet convinced of this total correlation p plus minus equals zero never you have plus one here and minus one they’re so it just like you of coins head on tails head or taste but if you get head here you are sure to get ahead here so it’s a total correlation okay so we have that because we are serious people and we want to make real measurements we are not happy just with and waving and saying a total correlation we want to have a real measurement of the level of correlation and for that we have a standard and classical definition we consider the result of measurement see as a random variable the result of measurement there as a random variable and we look at the correlation coefficient between these random variables classical definition average of the product minus the product of the average if there is no correlation this gives 0 and you normalize okay to have a number between plus 1 and minus 1 so when you do that you have a formula and now when you insert into this formula which is classical when you enter the prediction of quantum mechanics then you get a coefficient of coral correlation of polarization which is cosine of 2 times the angle between the polarizer whatever it is these a result you can check immediately that if the anger is zero you find one Total core is a correlation if the angle is 90 degrees you find minus one it is very easy to understand y minus 1 because if you since you polarize are crossed if you get +1 for the first polarizer you are sure to get

minus one for the other one so okay total correlation again etc so now we have a real prediction of quantum mechanics that we can test okay so this is redic shin and when you are a nice physicist like me I am really a physicist I like simple images you see okay strong correlation I don’t believe in magic and so I want to understand why I have a strong current okay this is my my job as a physicist when the sudden somebody turns on up here there is an effect there I want to understand why there is a correlation between the fact to turn a knob here and to have a result there so correlation I want to understand how can I understand it well the first idea is to say okay you have made a calculation look into the calculation and the calculation will give you an image well it turns out that it is not so simple because if you look at the direct calculation which implies doing a projection into the Hilbert space which is a tensor product of the space of the first photon by the space of the second button this is happening in an abstract Hilbert space very difficult to make an image in our real space okay so it’s annoying and I’d like to cite an important sentence in the book of Usher Paris usher Perez was a strong defender of the Copenhagen interpretation of quantum mechanics very Orthodox it was a very good theorists however if rights quantum phenomena do not occur in a Hilbert space they occur in the laboratory so I cannot be satisfied with an image which is only in a Hilbert space so let us try to make an image in real space and there is a way to do it and the way to do it is to assume that this polarizer is closer to the source than the other one so our first measurement here so I am in my lab here i can describe in the real space and the result of this measurement can be either plus 1 or minus 1 ok so let us suppose i get plus 1 what do i do now now i have famous collapse of the state vector by the way this calculation is absolutely orthodox ok it’s quaint energy approved ok I can show you all the pages of the book of current energy I am only using standard Orthodox quantum mechanics so after the measurement there is a famous collapse of the state vector and so what it tells me is that if i add the press for the first photon then immediately after this measurement the state of the two photon is prosperous ah now it’s interesting because now it’s a factorized state so if I i found this polarization for the first photon then immediately i know that the other one as the same polarization but if i affirm minus which means appendicular immediately after the measurement the other one is polarized perpendicularly that’s the way that the result of the calculation and now this result i can describe in our space okay and then the calculation you can continue because once you know that the second photon has a given polarization press in the first case or minus in the second case you just go on and then it’s just equation of applying the malleus row for the second measurement and then you find exactly the same result at the one it’s a little more complicated okay so if you are student and you take an exam it’s better to do the first calculation but if you want to understand maybe the second calculation is better and so what you get at the end that you get the same result as done with a direct calculation but there is a something strange the measurement on the first photon seems to influence instantaneously at a distance the state of the second photo so now I have an image an image in our state but there is something strange something that you know most of you know is called quantum nonlocality I do something here and instantaneously it seems that something happens they’re very bizarre and of course Einstein could not accept that because I’m shine you know causality relativistic causality etc okay so when you face this you say what can I do well in fact I can realize that there is another way for understand is correlation and this way of understanding correlation is very simple you have two objects which were created at the same place

then they travel they go away okay and you do a measurement here in a measurement there and you find correlated measurements obviously this can be related to the fact that the two object add a common property from the first moment when they were created think of medical doctors they look at some disease on twin brothers when they find that the disease as the same probability to happen for the twin brother they say okay the explanation is very simple they came they have the same genome the same chromosomes okay so there is a very simple idea for understand this correlation that when the two photons are emitted here they have a common property lambda and this common properties are the same value for lambda and when you make the measurement here it depends on lambda when you make the measurement there it depends on lambda so no surprise that you find the same reason for instance so this image is simple in convincing okay but board is agreed why did is DD disagree because when you invoke such an image which is really very natural very scientific okay but when you invoke such an image you complete quantum mechanics you say that the state vector is not enough all the pairs of photons are described by the same state vector but if I start saying that there are lambda parameters it means that certain pairs for instance at from the beginning polarized like that the other pairs which from the beginning a polarized like that etc so I see there are different kinds of pair so I see that I have to complete the formalism of quantum mechanics so this takes us back to the initial question isn’t it the case that quantum mechanics is only a statistical theory and we have an underlying level now we come to the conclusion that will understand the strange correlation we need to invoke this underlying level this was a point of view avenge time but Neil’s Bohr thought that it is impossible to complete quantum mechanics if you would complete quantum mechanics quantum mechanics would be more or less inconsistent the problem in this discussion between Einstein and Bohr is a following when you read n stein it is crystal clear so you are fully convinced that is right and when you read Niels Bohr it’s really impossible to understand what he means you know his famous this before that I mean it’s not a criticism is famous for that Niels Bohr was mumbling and having very long sentences and even when you read this paper it’s very difficult to understand i can tell you i’ve read all these papers about the pier debate okay Einstein is crystal clear Niels Bohr is impossible to understand there is it’s not a joke Niels Bohr once said you know it was always talking about complementarity complementarity of this and that etc and once he said that truth and clarity are complementary qualities ok and it is best to be as true as possible so clarity forget about it ok so the problem with this but what I can say honestly after reading all this text is that needs bore a deep intuition that he could not accept to complete quantum mechanics as Einstein wanted to do it but he could not demonstrate that it was impossible so what happened the debate between boring Einstein lasted until the death of these two great physicist really until the end of their lives they exchanged letters and they discussed is a visit of boring Princeton and discussing with Einstein ok but without much attention from a majority of physicist why not because they were still on look you are a young physicist there is a new theory quantum mechanics you apply to plenty of phenomena and this one it works wonderfully ok uke with quantum mechanics you can explain the mechanical properties of matter you can explain the electrical properties of matter you can explain the optical properties of matter you can explain everything chemical bonds etc etc so it’s really a fantastic theory you have heard that there is a discussion between Einstein and Bohr but look these are all guys ok good that they discuss especially because according to what you have heard of their discussion they don’t disagree on the calculations there only disagree on

the interpretation so you are an active physicist you use quantum mechanics you know that there is a debate but the debate is not about the mathematics so you use a mathematics that’s ok so we have to say that nobody cared ok about a few people well cutting her have been really writing about this but most of the other physicists did not case ok and then 30 years later well 29 but almost 30 John Bell came with a fantastic finding the finding was flowing if you believe in the interpretation do to understand if you believe that this correlation can be understood by invoking a common property between the two partners between the two particles then you have interesting consequence which is a quantitative consequence the idea is the following Bell writes the ID and in a very simple manner he says ok when the two photon are emitted there is a set of parameters that I called lambda lambda can be a complicated mathematical object doesn’t doesn’t matter ok now we admit that the result of measurement here depends on the value of lambda which is brought by this photo and depends on the orientation so you introduce a function capital a of lambda and of the orientation a which can take only two value plus 1 or minus 1 by the way nowadays erisa frenzy about bells inequality and regularly there are papers of people who say oh I have a strange result about bells inequality when dust and it it disagreed shows that bear was not right etc etc usually these people forget that we want to have a dichotomous function a function which can return only either plus 1 or minus 1 so this is crucial but it is what we get here when you send a photon on a polarizer you get either plus 1 or minus 1 you don’t get anything in between so similarly on the second polarizer you have a response which is a function with value plus 1 or minus 1 depending on lambda the same lambdas so first photon and the orientation be and of course you have to describe how the various pairs are created with a certain lambda or in order lambda and you describe it with the density of probability which is normal density of probabilities that is to say a positive and normalized a function and with this you can calculate for instance if you have the explicit value for this function you can calculate for instance the correlation of of polarization it’s not difficult to find that it is this value nothing else that the average value of the product a be ok let us take a very simple example let us assume that when the two photon are created are created with the same polarization whatever it means we think that we understand what is a polarization those are created with a certain polarization now I need to invent the function capital a well looks complicated but it is very simple if the polarizer is a line with the polarization of the photon we will find plus one if it is a 90 degree we will find minus 1 and if we are in between we put the frontier at 45 degrees so if the polarization of the photon is closer to the axis we get press 1 if it’s closer to the perpendicular we find minus 1 cannot get the simpler model ok in addition we assume that the distribution of the pair is fully isotropic why because we know that the quantum result is rotational invariance so we take something isotropic with this you make the calculation and you get the red line which is here this value of the coefficient of correlation calculated with this very simple model and you get this and the quantum result is cosine of two x so you see is not bad for such a simple model so then you go and you meet your friend which is an applied mathematician or theories he knows everything about Bessel function uncle function of this special function I tell him can you design a model with more sophisticated functions that would reproduce everywhere the prediction of quantum mechanics so is there a better model agreeing with quantum mechanics in our orientation and the answer is given by Bell serum and this is Bell theorem no there is no model which can reproduce all the prediction of quantum mechanics

how does it work what del Sol so there is no I will explain the words local hidden variable theory in the spirit of engine ID that can reproduce quantum mechanical prediction for our orientation so here is an example of what I mean by cannot reproduce for all orientations it reproduces here here here but here there is a slight difference okay so that the way it is how does it work what Bell could demonstrate is that if you assume that the correlation can be explained with lambdas capital n capital B not the special model any model with any form of lambda capital a capital B and function row then there is a quantity s which cannot be larger than to and which cannot be less than minus 2 and this quantity s is quite interesting a combination of for correlation coefficients considering to orientation a and a prime for the first polarizer and B & B prime for the second polarizer so you make a measurement a B then you make a be prime a prime B Prime and the last one is probably a prime B okay so you make four measurements okay you put the first number into this and according to this Bell CRM if you can understand this correlation and voc in supplementary parameter lambda this cannot be bigger than two on the other end remembers a quantum expression for the EPR situation it’s cosine of two x this angle so let us take this species this particular set of orientation a B equals pi over eight etc pi over 8 pi over 8 2 times pi over 8 is pi over 4 we are sure you follow me cosine of PI over 4 is 1 over root 2 so you get 1 over root 2 1 over root 2 1 over root 2 now look at a bit prime if you double the younger the cosine is minus 1 over root oh there is a minus sign so I have again 1 over root 2 so for the specific set of orientation the quantity s predicted by quantum mechanics is bigger than 2 and well theorem there is no model based on lambda a B etc which can reproduce all the prediction of quantum mechanics okay let us continue so now the possibility to complete quantum mechanics according to angela an ID is no longer a matter of taste test them into an experimental equation okay as somebody said if you find a conflict with quantum mechanics which is so well-established theory why don’t you consider again the demonstration of conflict so there are thousands probably hundreds of papers of people who try to see where does conflict it seems fair to me after reading not all of them but a large number of these papers that these are the necessary hypothesis to obtain bells inequalities that is to say to obtain a conflict with quantum mechanics first you must introduce the idea that each photon leaves or source with a property or a set of property determine that you can describe by a mathematical object lambda and the two-photon when they leave the sauce they have the same set that the idea of the wise you you I mean that the idea of understanding this correlation okay and the second idea is which is called the local rarest worldview is that the result of the measurement that you have here will only depend on the set of parameters lambda carried along by this photon and by the orientation of this polarizer and this is very important and it is local really swellview and then then realized when he was demonstrated is sin equality that in fact this imply what is called bells locality condition it implies that really the result of the measurement here is not allowed to it depend on the orientation of the other one if you if it could depend then you could not demonstrate bells inequality so this called bells locality condition but in the same paper there immediately notice

following fact is a look if while the two-photon are traveling from the source to the polarizer if you change rapidly the orientation of the polarizer then there is not enough time for this information to go to the other side so if you could change rapidly the orientation of the polarizer while the photon are in flight then this locality assumption would be guaranteed by the laws of relativity and clearly when you read understand there is always implicitly these hypotheses that when objects are space like separated in a relativistic sense then what you do here cannot instantaneously affect the other side so these what a bell says in his paper and now we have clearly a conflict between quantum mechanics and Einstein’s worldview the ancient walls view is called local realism that is to see the fact that when I have an object here I do a measurement here all the result of the measurement depends on the property of the object plus the setting of my measuring apparatus here and everything which is in the backwards light cone but not things which are out of the backward right code ok so now it’s time to go to an experimental test surprisingly in spite of all the wonderful achievements of quantum mechanics and all the wonderful experimental developments there was at that time no experimental result available to test bells inequalities and the reason if that best inequalities are extremely general basically any kind of correlation you can think of will obey quantum mechanics not only classical correlation like the twin brother with chromosome or if you have mechanical correlation that you can explain by classical mechanical classical electrodynamics but even correlations that you calculate with quantum mechanics in most of the case they don’t violate bells inequality it’s very rare that you find a situation which in which you predict a violation of bells inequality and so for this reason they realize that it is necessary to find the situation where the test is possible and this was a great achievement of krauser horn she money and all in 69 to show how with photon polarization you could find a situation which is exactly the situation that I have described there were three generation of experiment the pioneers in 72 there was one experiment in berkeley clouser and friedman one experiment in hob Alton Pipkin and it was very interesting because in 72 they go to posit results berkeley obtain the result in favor of quantum mechanics and violating bells inequality in hob they found agreement with bells inequality and disagreement with quantum mechanics then in 76 it was an experiment in Texas a and M you know what is a em agriculture and mining which is kind of interesting him but you know they were in the in the in the center so they say say and in this experiment they found quantum mechanics the problem with all these experiences that if I would describe them you would not recognize the schemes that I have shown I mean at that time use the technology the experiments were quite different from the ideal scheme which means that you need supplementary hypothesis moreover in the first experiment the rate of data was so low that it took weeks to accumulate the data so let’s say it was wonderful experiment but it’s not really surprising that they were conflicting result these 175 I am backed into a series of experiment and the goal was to build a source of entangled photon extremely efficient in order to allow me to do measurements in schemes closer and closer to the ideal scheme and I will describe it so this experiment were completely lady to us Massimo said it was my PhD thesis and then a new generation of experiment started by the end of the 80s with new type of sources of entangled photon and it’s still going on and I will say a few words about that so let us say a few words about the experiments I developed for my PhD thesis the main idea was a following this is the scheme producing the two entangled photon that had been discovered by clauser and company so the

idea that if you can excite an atom in that case it calcium doesn’t matter with an angular momentum J core 0 and wait it will it will decay sruti equal 1 and j equal 0 and then because there are two different path to decay what you obtain is a linear superposition of this which is a sigma plus sigma minus polarization plus that which is siva buying a sigma plus and when you express the circular polarization as a function of the lily of the linear polarization you get exactly the sake you won’t work the difficulty is to excite this state you in the original experiment you cannot do it by direct action of an ultraviolet photon because the two level of the same parity and so what they did was exciting the atom to upper line level and waiting and when they waited from time to time there was a nut on decaying through this route and they got a pair of entangled photon but quite most of the time there was another route and then finally it came here and you had the second photon but not the first one so it was a very inefficient sauce and plenty for the other problems with the sauce so what I did because of the progress of Technology there were the new laser there were tunable laser what I did was exciting directly this transition by adding two photons the two level of the same parity so I can affect a two-photon transition at that time it was really state-of-the-art and it worked and the sauce was beautiful I told you that in the experiment of krauser it took days and weeks to have significant result look how many i odd i obtained hundred real coincidence per second which means in only 100 second less than two minutes i attend to the fourth 10 to the 4 7th minja the statistical accuracy is already one percent okay because a statistical spread is root okay so in two minutes I had one percent accuracy which was wonderful okay so with this what did we do first I repeated the experiment of the other people so I don’t described in details but I the idea is the following when you were discussing with theorists there were a series that would say look entanglement we know it for instance in the helium atom we know that the two electrons are entangled if we would not write the fact that the two electron are entangled we would not have the right levels for the idiom Adam bet you know my friend my young friend I was still young at that time you know my young friend entanglement is a property of the microscopic world when you go to macroscopic distances it will disappear say aha very interesting what is the scale what is a macroscopic distance and then the guy would scratch his head and say mmm coherence length of the wave packet describing the photo perfect because here the lifetime is 500 a second which means the Koreans length of 1.5 meters so I pulled my polarize at six matter from the source and tangle man was still there violation of bells inequality so the violation of bells inequality that my colleagues are found a short distance I found it at long distance but it was still a scheme far from the ideal one now comes the gorgeous experiment while the two cuadras x-ray now I could obtain at that time polarizer beam splitters you are going to tell me how I can buy it on on a catalog yes at that time you could not buy it on a catalog between you and me I had to bribe a friend with flips labs in I’d oven and they produce it for me and I say how much do I owe you say you cannot pay it well beyond what you can pay with University so I got it for free or maybe a couple of bottles of wine and something like that ok so I add real polarisers giving result + 1 + minus one this was totally new in previous schemes they only add the police one result they did not have the minus one result the big advantage is the following in a single measurement with orientation a and B you get the phone numbers plus plus plus minus minus plus and minus minus so here the murderer coefficient of polarization is nothing else that this expression divided by the Sun itself normalizing measurement you don’t need any accessory calibration you know the experiment is calibrating itself at each measurement this is really a fantastic advantage and

with this I just I like to in the context of this metrology discussion the curve which is here the green curve had been calculated beef before doing the measurement it’s a prediction of quantum mechanics taking into account so small the effects of the experiment that is to say I had measured the small inefficiencies of the polarizer and also when you have finite solid angle there is a complicated calculation that shows that what you predict is a contrast slightly less and what this predict in the ideal case so the green curve is a prediction of quantum mechanics as a real experiment and the box is here at the result of the measurements with plus or minus two standard deviation you see a beautiful it is there is a perfect agreement with a result of canto makin between the result of the measurement and the prediction of quantum mechanics now this curve also allows me to emphasize why it is rare that you can buy eight bells inequality let you post you don’t know about bells inequality and somebody say are you should test correlation of polarization what angle are you going to select 0 degree 45 degrees 90 degrees okays at the first reaction 0 degree there is no conflict between quantum mechanics and bells inequality 45 degrees no conflict between it’s certainly not beyond to 90 degrees no conflict in fact I have been an experiment of that kind with gamma photon emitted nice disintegration of positronium by people who did not know bells inequality and because it was a very long experiment that I made the measurement at zero degree 45 degrees and 90 degree nothing you could draw if you don’t know bells inequality you don’t know that you should end system this point but if you insist on this point then you get a violation of bells inequality by more than 40 standard deviation this is impressive it’s more than the Higgs boson okay okay last 50 minutes I have one hour mr. chairman yeah I have a chronometer he it’s a quantity it’s an atomic clock and 50 minutes I thought you remember in order to have a real conflict with relativity you want to rotate the polarizer while the photo 9 flight in my experiment the distance between here and there was six matter which represent 20 nano second so can we rotate this which is a big system with shield led the shielding etc 40 40 kilogram you cannot rotate a polarizer 40 kilograms in 10 nano second or less okay so what we did is developing a switch here an acousto-optic switch that can either let light go straight or redirect light on the side and so with this switch which can switch every 10 nano second okay then you send either the photon to a polarizer in orientation a or to a polarizer in orientation a prime and this is equivalent with a single polarizer switch from a to a prime back to way back to a prime etc same on the other side the experiment is not perfect the time is ok the timing is ok ok we switch every 10 nanosecond it take 40 nano second to go from here to there so the tiny is okay what is not okay is the fact that it is a regular switching in an ideal experiment you would dream of random switching we were not stupid the generator here was different from this one it was even a different frequencies his one was about 20 megahertz is one about 25 minutes moreover they were not well stabilized generator so there was some kind of randomness between here and there but it’s not a real random number generator we did the experiment this is at the acousto-optic switch that I had to be no company could deliver so I had to build it myself and the signal was reduced so rather than having a significant result in two minutes it took half an hour so we decided to stop to to take the data when we had a violation of bells inequality by six normal deviation which is significant we could have continued to accumulate data but you know they were adrift standing like that I think six standard deviation was really the meaning of our experiment it was a first experiment where Angela and causality was involved so I told you there’s been a third generation of experiment to make

a long story short the big progress that was found in the between 85 and 95 it took 10 years to develop the new source the big progress is a following in my experiments the atoms are emitting photon in any direction of space so you have to collect the beam in big lenses and we have what we call in French large item do okay the product of the solid angle by the surface okay with a nonlinear process parametric down-conversion you can enforce a phase matching condition in which you convince the photons to be emitted in a well-defined direction so the photons are emitted in your small item do and then you can feed the photon in to optical fibers and once you have put the photon into an optical fiber you can make experiments at a distance of tens of kilometers Nicola she sang in Geneva is making experiments at tens of kilo meta because he is allowed to use a commercial network of optical fibers at night at night Swiss people sleep and ecology Zhang is doing measurement on the on the network zeilinger in an n reg arise in invoke at that time made an experiment also with optical fiber and they could implement for the first time a setup in which the direction of the polarizer was chosen by a real random number generator they confirm the result that I have obtained in 82 ok I don’t want to detail the discussion about loopholes what are loopholes loopholes are hypotheses necessary to be able to compare bells inequality tests to the ideal bells inequality people there have been plenty of discussion people have shown that there were two possibility that a hidden variable theory could give the result of quantum mechanics due to two problems the first one was in the static experiment the fact that there was a possibility of an exchange of information between the two ends of the extra man this is named the locality RuPaul the locality loophole has been closed by the experiment i did in 82 by the experiment that i linger advice did in 98 ok the other RuPaul is a fact that the detector of photon have poor efficiency of quantum efficiency of twenty percent thirty percent so if somebody is a determined advocate of hidden variable theories it can use this the fact that many photon are lost to invent and theory in which the photon which are lost do not behave in the same way as a photon which are not lost and so this is called the sensitivity sensitivity report the sensitivity report has been closed a few years ago by using this fantastic detector like the one you are developing here with supra conductors detector now we have their detector of photon with efficiency of how much ninety-eight ninety-nine percent ok so the sensitivity report has been closed and then the advocates of hidden rebel theory come and see ah but the loopholes have not been closed similar nursery so now there is an experiment which is being published which has been performed in Delft which is complicated experiment with entanglement swapping and V centers and thing like that and i can tell you i don’t know if it has been published yet or not but I know the preprint they have V between quad ultimate experiment in which all the reports are closed simultaneously they find agreement with quantum mechanics and a violation of bells inequality by only two standard deviation so it’s fine because it’s a wonderful experiment if we do not have all the previous results nobody would believe to standard deviation on the other hand it’s a beautiful scheme they show that it is possible to make a test without closing all the reports and I have no doubt that in the coming months and years there will be more and more results on that so we can conclude that Einstein’s local realism is untenable and to conclude with the chairman it is you the chairman did you Massimo ah well that’s okay I can go on my keyboard no nose is very important what should we conclude we should conclude that local realism is untenable and Einstein

himself wrote what is a conclusion so you should be surprised and say come on Einstein did not believe in what he was expressing yes he was believing but he was making a reasoning ad absurdum he would tell us if fine was not right this is what would happen but we know that in this is is not right there is a violation of bells inequality and so this is what we have to conclude either drop the need of the independence of the physical reality present in different part of space when he say space means space-time okay or accept that the measurement on the first system changes instantaneously is a world of Einstein himself the real situation of the other object this is called quantum nonlocality so Einstein tells us that we have to accept quantum nonlocality some people call it quantum holism it’s very important for the following reason to understand these words quantum ilysm tells us that when I have a pair of entangled object I am NOT allowed to consider that the property of the wall system is the reunion of the properties of the first one and of the second one there is more in a pair of entangled object that the sums of the properties of the first one and the second one why is it important to understand that it’s because it is at the root of quantum information quantum information is basing the factor when you have entangled object there is much more in the end tunngle system than in the sum of the individual properties so in one minute I show you what I have plan to say are we leaving a new quantum revolution quantum information is based on entanglement so quantum cryptography quantum cryptography with entangled pairs so you know the idea of quantum photography the two friends Alice and Bob and the o fool eavesdropper who tries to enter set and the basic idea that the laws of quantum mechanics ensures the security it’s not a technical difficulty that you need to be computer to factorize number it’s basic laws of quantum mechanics which ensures the security if you ask me equation i can answer quantum computing computer nobody knows if it will work the quantum computer quantum simulation it all already works in particular in the in the lab of Massimo quantum metrology you all know the Virgo interferometer if you use squeezed light you increase the sensitivity of the VR goin T parramatta it costs less money to produce quiz light and put it in the end of row meta than building a 10-kilometer rather than two kilometer and the Pharaoh meta atomic rock no atomic clock here here gravimeter based on ultracold atoms all this is quantum energy here NV centres to measure magnetic fields beyond standard possibilities so to make a long story short I want to tell you that in my opinion the two ingredients which are the root of this new quantum revolution is not only entanglement I’ve emphasized entanglement which is new and different from wave particle duality but it is also the fact that in the last decades experimentalist I’ve learned how to control individual quantum objects this was beyond what people believed in the 50s in the 50s people thought you have zillions of quantum object and you can make only measurement on began samples but here you know FM atomic force microscope producing single photon trapping a single atom or single electron looking a quantum jumps etc etc so the new quantum revolution in my opinion is based on entanglement and on the control of individual quantum objects in contrast to the first quantum revolution which was based on wave particle duality and large ensembles and if you remember what was the first quantum revolution it works first conceptual but it also gave us the laser the transistor the computer it gave us the information and communication society it was not only conceptual but also technological so you can ask the question will quantum information and quantum technology to the quantum engineering society that we are going to discuss tomorrow in Brussels the most likely roadmap is from proofs of principle with well-defined

elementary microscopic objects photon Adam ions to solid state devices it’s fascinating we live exciting times I thank you very much for your attention you