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AIP conference proceedings

Quantum-to-classical transition via fuzzy measurements on high gain spontaneous parametric down-conversion

Nicolò Spagnolo, Chiara Vitelli, Lorenzo Toffoli, Fabio Sciarrino, F. De Martini, Timothy C. Ralph, Ping Koy Lam

Published Jan 1, 2011• 1 citation
Publisher

Abstract

We analyze the high gain spontaneous parametric down‐conversion in a non collinear geometry as a paradigmatic scenario to investigate the observation of nonlocal properties when the size of the system is increased while keeping fixed the measurement resolution. We observe theoretically a fast decrease in the amount of Bell’s inequality violation when the number of particles is increased, due to the low resolution of the measurement apparatus. This theoretical analysis is supported by the experimental observation of macro‐macro correlations with an average number of photons of about 103. Our results enlighten the practical extreme difficulty of observing non‐locality by performing such a dichotomic fuzzy measurement.

DOI
10.1063/1.3630193

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We analyze the high gain spontaneous parametric down‐conversion in a non collinear geometry as a paradigmatic scenario to investigate the observation of nonlocal properties when the size of the system is increased while keeping fixed the measurement resolution. We observe theoretically a fast decrease in the amount of Bell’s inequality violation when the number of particles is increased, due to the low resolution of the measurement apparatus. This theoretical analysis is supported by the experimental observation of macro‐macro correlations with an average number of photons of about 103. Our results enlighten the practical extreme difficulty of observing non‐locality by performing such a dichotomic fuzzy measurement.
We consider the high-gain spontaneous parametric down-conversion in a noncollinear geometry as a paradigmatic scenario to investigate the quantum-to-classical transition by increasing the pump power, that is, the average number of generated photons. The possibility of observing quantum correlations in such a macroscopic quantum system through dichotomic measurement will be analyzed by addressing two different measurement schemes, based on different dichotomization processes. More specifically, we will investigate the persistence of nonlocality in an increasing size n2\frac{n}{2}2n​-spin singlet state by studying the change in the correlations form as nnn increases, both in the ideal case and in presence of losses. We observe a fast decrease in the amount of Bell's inequality violation for increasing system size. This theoretical analysis is supported by the experimental observation of macro-macro correlations with an average number of photons of about 103{10}^{3}103. Our results shed light on the practical extreme difficulty of observing nonlocality by performing such a dichotomic fuzzy measurement.
Bell nonlocality and quantum contextuality are two important resources which, however, behave very differently in many tasks where the quantum correlation has an edge over its classical counterpart. In this work, we directly compare these two behaviors, which via the Cabello-Severini-Winter graph-theoretical approach, can be associated with a same exclusivity graph. In particular, we consider the exclusivity graph that leads to I3322{I}_{3322}I3322​-type inequalities in the Bell and the contextual scenarios, respectively. We find that maximal violation of Bell inequality is around 6.251, and maximal violation of the noncontextuality inequality is around 6.588 for a five-dimensional system and 6.571 for a four-dimensional system, respectively. The results predict a gap of $\mathrm{\ensuremath{\Delta}}\ensuremath{\approx}0.32$ between quantum contextuality and Bell nonlocality. We then present an experimental observation of the gap by employing both the maximally entangled photon pairs from the spontaneous parametric down-conversion process and the single photons encoded into qudits from an intrinsic defect in gallium nitride. Our results will further deepen the understanding of different types of quantum correlations.
We consider travelling-wave parametric down-conversion in the high-gain regime and present the experimental demonstration of the quantum character of the spatial fluctuations in the system. In addition to showing the presence of sub-shot noise fluctuations in the intensity difference, we demonstrate that the peak value of the normalized spatial correlations between signal and idler lies well above the line marking the boundary between the classical and the quantum domain. This effect is equivalent to the apparent violation of the Cauchy–Schwartz inequality, predicted by some of us years ago, which represents a spatial analogue of photon antibunching in time. Finally, we analyse numerically the transition from the quantum to the classical regime when the gain is increased and we emphasize the role of the inaccuracy in the determination of the symmetry centre of the signal–idler pattern in the far-field plane.
We consider travelling-wave parametric down-conversion in the high-gain regime and present the experimental demonstration of the quantum character of the spatial fluctuations in the system. In addition to showing the presence of sub-shot noise fluctuations in the intensity difference, we demonstrate that the peak value of the normalized spatial correlations between signal and idler lies well above the line marking the boundary between the classical and the quantum domain. This effect is equivalent to the apparent violation of the Cauchy-Schwartz inequality, predicted by some of us years ago, which represents a spatial analogue of photon antibunching in time. Finally, we analyse numerically the transition from the quantum to the classical regime when the gain is increased and we emphasize the role of the inaccuracy in the determination of the symmetry center of the signal/idler pattern in the far-field plane.
In recent years parametric-down-conversion photon sources have been proposed and used to test local realism via Bell-type inequalities. This study shows that this technique fails to discriminate between quantum mechanics and local realism in all those tests in which polarization correlations are measured, since dichotomic observables cannot be associated satisfactorily with the state produced in these experiments. A more adequate description of these photon sources leads to an alternative inequality for Einstein locality, which is always satisfied by quantum-mechanical predictions. The result can be extended to all the experiments in which only one-half of the emitted pairs are detected.
Nonlocality is one of the main characteristic features of quantum systems involving more than one spatially separated subsystem. It is manifested theoretically as well as experimentally through violation of some local realistic inequality. On the other hand, classical behavior of all physical phenomena in the macroscopic limit gives a general intuition that any physical theory for describing microscopic phenomena should resemble classical physics in the macroscopic regime, the so-called macrorealism. In the 2-2-2 scenario (two parties, with each performing two measurements and each measurement having two outcomes), contemplating all the no-signaling correlations, we characterize which of them would exhibit classical (local realistic) behavior in the macroscopic limit. Interestingly, we find correlations which at the single-copy level violate the Bell-Clauser-Horne-Shimony-Holt inequality by an amount less than the optimal quantum violation (i.e., Cirel'son bound 222\sqrt{2}22​), but in the macroscopic limit gives rise to a value which is higher than 222\sqrt{2}22​. Such correlations are therefore not considered physical. Our study thus provides a sufficient criterion to identify some of unphysical correlations.