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Journal of the Optical Society of America B

Einstein–Podolsky–Rosen quantum simulations in nonclassical phase-space

Simon Kiesewetter, K. Dechoum, Bogdan Opanchuk, L. Rosales-Zárate, M. D. Reid, P. D. Drummond

Published Mar 31, 2015• 0 citations
Publisher

Abstract

We give a brief history of probabilistic quantum simulations of Einstein–Podolsky–Rosen paradoxes. This treats the early origins of the modern proposals using continuous variables, simulation methods using the positive-P representation, and current developments. Recent simulations treated include the behavior of parametric downconversion near the critical point, the simulation of parametric Bell violations, quantum entanglement, and correlations in optomechanics, as well as extensions to quantum field systems with planar interferometers.

DOI
10.1364/josab.32.000a64

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We give a brief history of probabilistic quantum simulations of Einstein–Podolsky–Rosen paradoxes. This treats the early origins of the modern proposals using continuous variables, simulation methods using the positive-P representation, and current developments. Recent simulations treated include the behavior of parametric downconversion near the critical point, the simulation of parametric Bell violations, quantum entanglement, and correlations in optomechanics, as well as extensions to quantum field systems with planar interferometers.
This Colloquium examines the field of the Einstein, Podolsky, and Rosen (EPR) gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bell's theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.
Quantum simulations of Bell inequality violations are numerically obtained using probabilistic phase-space methods, namely, the positive-PPP representation. In this approach the moments of quantum observables are evaluated as moments of variables that have values outside the normal eigenvalue range. There is thus a parallel with quantum weak measurements and weak values. Nevertheless, the representation is exactly equivalent to quantum mechanics. A number of states violating Bell inequalities are sampled, demonstrating that these quantum paradoxes can be treated with probabilistic methods. We treat quantum dynamics by simulating the time evolution of the Bell state formed via parametric down-conversion and discuss multimode generalizations.
This Colloquium examines the field of the EPR Gedankenexperiment, from the original paper of Einstein, Podolsky and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. We analyze the relationship with entanglement and Bell's theorem, and summarize the progress to date towards experimental confirmation of the EPR paradox, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fibre quantum soliton experiments. We discuss current proposals for extending EPR experiments to massive-particle systems, including spin-squeezing, atomic position entangle- ment, and quadrature entanglement in ultra-cold atoms. Finally, we examine applications of this technology to quantum key distribution, quantum teleportation and entanglement-swapping.
In 1935, Einstein, Podolsky and Rosen published their influential paper proposing a now famous paradox (the EPR paradox) that threw doubt on the completeness of quantum mechanics. Two fundamental concepts: entanglement and steering, were given in the response to the EPR paper by Schrodinger, which both reflect the nonlocal nature of quantum mechanics. In 1964, John Bell obtained an experimentally testable inequality, in which its violation contradicts the prediction of local hidden variable models and agrees with that of quantum mechanics. Since then, great efforts have been made to experimentally investigate the nonlocal feature of quantum mechanics and many distinguished quantum properties were observed. In this work, along with the discussion of the development of quantum nonlocality, we would focus on our recent experimental efforts in investigating quantum correlations and their applications with optical systems, including the study of entanglement-assisted entropic uncertainty principle, Einstein-Podolsky-Rosen steering and the dynamics of quantum correlations.
A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between spatially separated subsystems is not perfect. Two types of criteria for EPR correlations are determined. The first type are based on measurements of the variances of conditional probability distributions and are necessary to reflect directly the situation of the original EPR paradox. The second weaker set of EPR criteria are based on the proven failure of (Bell-type) local realistic theories which could be consistent with a local quantum description for each subsystem. The relationship with criteria sufficient to prove entanglement is established, to show that any demonstration of EPR correlations will also signify entanglement. It is also shown how a demonstration of entanglement between two spatially separated subsystems, if not able to interpreted as a violation of a Bell-type inequality, may be interpreted as a demonstration of the EPR correlations. In particular it is explained how the experimental observation of two-mode squeezing using spatially separated detectors will signify not only entanglement but EPR correlations defined in a general sense.