 So, first, speaking of the absence, actually, in macro-media, we talked about measuring non-computing of services, the significant motor-wise effects would be very useful for innovation. Okay. Thank you, Chairman. First of all, let me thank the organizer for their kind invitation for the beautiful organization of this fantastic workshop and school. Today, I will introduce you to some experiments we recently performed in our quantum optics labs in Torino, the north of Italy. The name of the institute is Instituto Nacional di Ricerca Metrologica, so we are a meteorological center of the search. And briefly, today, adding another experiment to the one reported in the title of the talk, I will introduce you also to another quantum measurement paradigm whose name is Protective Measurement, with which we recently obtained very nice results, published last month. So, each experiment I will talk to you about today is related to a particular non-Orthodox quantum measurement paradigm, and the name is Week Measurement. So, briefly, to introduce you in a short way this kind of paradigm, I inserted here the seminal paper with which Arno Valberg and Weillmann reported on this kind of type of quantum measurement. Briefly, the Week Measurement, thanks to the Week Measurement, we can provide some information softly disturbing the evolution of the system, so preventing the collapse of the wave function. And thanks to the weakness of the interaction, we obtain a very particular result that sometimes are very weird. In particular, the authors in the theoretical paper, this reference is here, consider the case in which Week Measurement take place between two strong conventional measurements that they call the pre- and post-selected states. So, we have an initial state and a final state. And so, if we want to evaluate an observable of the system, represented in this case by the median operator, A, the definition of the Week Measurement gives and of the Week Bays, give this form. Typically, in the Week Measurement approach, we exploit the common von Neumann coupling between an observable, in this case, A, and a pointer observable, let's say the momentum of the needle of the measurement apparatus. And the unitary operation is this, where G represents a real coupling system, and A and P are the two observable. In this framework, the correlation are generated between the shift of the pointer and the quantum system through this von Neumann approach. After that, we post-select, so in a strong way on the final state, and the overall state at the output of this procedure takes this form. Let's take in mind that here, we are considering the momentum, and you know that X is a canonical conjugated operator to the momentum, so the position of the needle of the measurement apparatus, and in this kind of paradigm, if we measure this value, so the shift in the pointer of position, we see that, performing the calculation, X is related to the real part of the weak value. I say the real part because weak values are particular objects, in fact, they are complex, complex number, and moreover, they are unbounded, so in contrast to the standard quantum mechanical expectation values, weak values are not constrained to lie within the extreme of the agent value spectrum, and despite the fact that this can be counterintuitive, the prediction of this formula follows directly from the calculation of the quantum mechanics. I have not to say that this is something like weird stuff, and here you see a lot of paper in which discuss the interpretational issues of this approach, and if someone is interested in, I suggest in particular this review that gives a very good overview of the problem. Anyway, for an experimental point of view, they are anyway interesting because we can extract some very nice information following this approach. In particular, the bibliography is very rich about this, and the field of applications are spans from metrology, from national quantum mechanics, and also quantum optics. The experiment that I will introduce you now deal with this kind of measurement, so pure quantum optics experiment, exploiting the birefringent effects on photopolarization. So to briefly recap the situation, in a strong measurement we have, using a birefringent crystal, a photon with a certain unknown polarization that enters into this crystal, birefringent crystal, and depending on the polarization of the entering incoming particle, we have this situation at the output. So this is a strong measurement. In fact, we have a collapse of the wave function. In the other approach, in the weak measurement approach, the information given by the weak measurement is not fully described, but the initial state does not collapse. And so it is ready for a second measurement that could be strong or again weak. So you see that there is an overlap between the two beams, at variance with this case. This case is something like a Stern-Gerlach apparatus in an optical version. If after this first weak measurement, we implement a sharp measurement, again we have the wave function collapse. And so it is not possible to simultaneously evaluate to non-commuting observables. But in this other paper by Michison, Josiah and Popescu, they say that with this weak measurement approach, it is possible to release this strict bound in order to perform a measure on different variables in sequence. And so this opened the door to other measurement that can be joined with measurement. And this is the proposal. And also sequential with measurement. So today I will talk about the sequential. And in particular, we have to experimentally evaluate this formula. So our setup was something like this. So we have an initial state, psi e, that enters into the experiment in this direction. So here we have the first weak interaction. And here we have projection on vertical state of polarization. After that, the photons enter into the second block of measurement, again weak measurement. That now is operated in order to have a projection on this direction, psi, always again linearly polarized, but has an orientation that makes these two operators not orthogonal. So in principle, not evaluable. The aim of this kind of setup is to measure x that is related to the weak values of psi p, y that is related to pi b, and the covariance of x and y. Because due to the fact that we can measure these by evaluating the position of the first measurement apparatus and the same with the second measurement apparatus. And obviously we are able to measure this part, this term. Inverting this relation, we are able to obtain the sequential weak values of this term. The experimental setup is something like this. We have a mod-locked laser, femtosecond operating femtosecond regime, a second harmonic generator that gives a pump central wavelength around about 400 nanometers. And this pump enters into an online air crystal in order to give a parametric down conversion emission. So we have at the output two correlated beams, two entangled photons. And on one branch, we take the trigger. So in this part of the setup, we have the trigger. So the single photon enters into the fiber, goes to a single photon detector that opens a gate on this particular spada ray camera that I will describe you in a while. And this signal heralds the arrival of the correlated photons on the other branch. So here we have a coupling of the single photon into a single mod fiber. And the light is going into this part of the experiment. Into this part of the experiment. Here we have the pre-selection of the state, linear polarization. Here the first week measurement operated by a birefringent crystal. The second crystal is just inserted because here we have the polarization that splits vertical from horizontal. But this spatial workoff has also a temporal workoff. So due to the fact that the group velocity is different with respect for the propagation of the two polarization inside the crystal, we have that, in principle, the two channels at the output have some time delay. So these compensate for this delay. After that, the photon, the single photon, enters into the second block of measurement. These and these are two halfway plates that are inserted in order to orient the polarization of the photon in a non-orthogonal direction with respect to the first one. And after that, we have a post-selection. You see that the g2 value of the source gives a result that is very high. So this is pure single photon source. And the rallying detection is about 100 kilohertz and the integration window of the camera is about six nanosecond. This is the device. So in a nutshell, this is a particular CCD camera in which each pixel is a real single photon. Detector, so it's a prototype realized by Polytechnic of the Milano. It's not on the market now. And these is a typical measurement data acquisition and you see that each block is a single detection. And you see that the reconstruction of the beam with respect to the theoretical simulation have a very high fidelity. Briefly, to move to the experimental results, we see that we obtain very nice data points. This region, the blue region, represents the bound region of the eigenvalues. And you see that sometimes, okay, the red blocks refer to these values, experimental values. And you see that sometimes you can have some experimental data that is outside the bounded area, the bounded zone represented by the spectrum of the eigenvalues. And sometimes you see that, for example, in this case, we have some data that are close, very close to zero, and other are negative. Despite the fact that, in particular, we have a negative value for this object. And despite the fact that one is zero and the other is positive. We check it also for consistency of these weak values. And we found that, with respect to the theory, we obtained, considering also the uncertainty, a very, very good result. So weak values and weak measurement represent for us an intriguing paradigm to be investigated. So, due to reason of time, I switch to the second part of the talk in which I will introduce you another intriguing paradigm whose name is protective measurement. Very weird for some aspect. And so, in order to introduce this paradigm, I say before that, as you know, in standard quantum mechanics, when we have an initial state, psi, wave function, and we want to evaluate an observable A, we can associate a definite number to this object and the meaning of this number is purely statistical, because to find expectation value of the observable, we have to measure an ensemble of identically prepared particles a lot of time. In another seminal paper always by Aronov and Weidman, they proposed a particular paradigm that they called protective measurement that is very weird. So in some sense, they proposed that it is possible to find expectation value of an observable by measuring only one single particle. Obviously, with respect to the standard quantum mechanics, this is very weird. And obviously, a controversial issue was raised up. So again, we have a lot of paper debate about this argument, whose main point was with this procedure, we observe the state or only the protection mechanism. Okay, up to now, there is no answer. The fight is still open. Anyway, on the experimental point of view, we decided to investigate deeper this kind of approach. And due to the fact that an experimental implementation of this paradigm was missing, we decided to implement a particular variant of this protection paradigm that is active and is based on the Zeno effect. And in particular, as it will be clear later, in our Zeno protection method, we end the project on a particular state. So I recap the projective measurement. We have an initial state entering into a birefringent crystal. And here we have a strong measurement. This is the operation operator that described the interaction. And the global state composed by the state and measurement apparatus evolves in this way. You see that here we have something like an entanglement between the system and the measurement apparatus. Here, the observable that we want to evaluate is this one, so something that discriminates from horizontal to vertical polarization. And this is the standard scheme, the Stern-Gerlach. So we have some photons will fall down here, other here. In the protective scheme, let's concentrate our attention to a single step at the beginning. We have a different setup. Here, we perform a weak measurement. So with respect to the stronger, the crystal will be thinner. And when the photon goes out from this thin crystal, we insert a Xeno-protection, operated in this case by a thin polarizer oriented on the side direction. And we repeat this scheme, this fundamental scheme, and times, in principle, the theory say that these steps has to tend toward infinite. Obviously, in an experimental implementation, we will have a finite number of steps. Anyway, in this case, you see that the evolution of the global state returns out is a kind of equation in which there is no more entanglement. And in principle, also with the considering the measurement on one particle, we can gain information about the expectation value of the observable. Obviously, when we consider number of single particles, we can increase the precision of the measurement. But anyway, in principle, it is possible to extract some information only considering one single particle. The experimental setup is almost the same for what concerns the source, the pump of the single photon source, let's say. But now, the heralded single photon is prepared in this block. And after that, we have, again, a weak measurement crystal, a second crystal, again, compensated for temporal walk-off. And now, here we have a polarizing plate that operates the protection. The spatial mode comes out from the single mode fiber is close to Gaussian with a special distribution of about four pixels. And this block introduces a separation between the two polarizations of about one and a half pixels. So this is less than the beam width. If we repeat this fundamental block K times at limit to infinite, but for space reason and also money reason we reduce from infinite to seven steps. But anyway, it was sufficient for us to observe what we want to observe. We obtained this result. So on the camera, this is the display of the camera, each point represents one single photon. And this is the distribution when the protection is not active. So there is not the polarizing plate. When we insert this protection, this Xenoprotection, we see that the distribution focuses very close to the expected theoretical value. Here, we performed this experiment with an initial state of this shape. The theoretical value we had to measure was this. And with our implementation, we obtained experimentally this value that considering also the uncertainty, it's very close to the theoretical value. Taking only one frame of this camera, you see that this is a single photon. You see that with this procedure, it is possible to extract the expectation value of the polarization of the photon by means of a measurement performed on a single protected photon. These are the results with a huge number of photons with different initial states. And just in order to conclude, I just mentioned that this kind of protection scheme is something like this quantum information protocol where Bob wants to measure the expectation value of an observable state that is unknown to him. In present of a protection mechanism designed for such state. So the state together with the protection mechanism is prepared by Alice who knows obviously the state to set up the protection. And does Bob measure the photon in conjunction with the protection apparatus? So this is just to recap another intriguing result that is going to be published. And just to summarize what I reported in the first part I introduced you some particular measurement related to weak values in particular the possibility to operate an experimental implementation of sequential weak values. And in the second part we implemented something like a more complex protocol in order to test what in literature is called protective measurement. Obviously these experiments are again because we want to go deep into this kind of research but for the moment here you find the reference in the case you are interested in this kind of weak measurements. So thank you for your rotation. This is the group in which I work and the theoretical group is composed by Elio Cohen from Bristol and Lev Meinman from Tel Aviv University and the special single-photon array camera is has been invented and produced by Polytechnico Milan in collaboration with microphotons devices. So thank you for your attention and I thank the organizer for the invitation. Thank you.