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Physical Review A

Optical simulation of adaptive nonlocality distillation

Wen‐Jing Chu, Ming Yang, Guo‐Zhu Pan, Zhuo‐Liang Cao

Published Oct 23, 2018• 1 citation
Publisher

Abstract

An optical scheme for simulating adaptive nonlocality distillation is proposed. In the asymptotic limit, arbitrary correlated nonlocal boxes can be distilled to the maximally nonlocal one, i.e., the Popescu-Rohrlich box [S. Popescu and D. Rohrlich, Found Phys. 24, 379 (1994)]. The major obstacle in simulating the adaptive nonlocality distillation scheme, proposed by Brunner and Skrzypczyk [N. Brunner and P. Skrzypczyk, Phys. Rev. Lett. 102, 160403 (2009)], is how to simulate the nonlocal boxes with a quantum system and to get the output of each box without destroying the quantum state simulating it. Here the nonlocal boxes are simulated by appropriately pre- and postselected polarization entangled photon pairs. The output of the first box is measured without destroying the quantum state, simulating it by exploiting a quantum nondemolition measurement, which is realized by a standard quantum teleportation process. This scheme provides a feasible tool for the experimental study of the manipulation of nonlocality in the postquantum regime and the exact physical principle precisely distinguishing physically realizable correlations from nonphysical ones.

DOI
10.1103/physreva.98.042123

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An optical scheme for simulating adaptive nonlocality distillation is proposed. In the asymptotic limit, arbitrary correlated nonlocal boxes can be distilled to the maximally nonlocal one, i.e., the Popescu-Rohrlich box [S. Popescu and D. Rohrlich, Found Phys. 24, 379 (1994)]. The major obstacle in simulating the adaptive nonlocality distillation scheme, proposed by Brunner and Skrzypczyk [N. Brunner and P. Skrzypczyk, Phys. Rev. Lett. 102, 160403 (2009)], is how to simulate the nonlocal boxes with a quantum system and to get the output of each box without destroying the quantum state simulating it. Here the nonlocal boxes are simulated by appropriately pre- and postselected polarization entangled photon pairs. The output of the first box is measured without destroying the quantum state, simulating it by exploiting a quantum nondemolition measurement, which is realized by a standard quantum teleportation process. This scheme provides a feasible tool for the experimental study of the manipulation of nonlocality in the postquantum regime and the exact physical principle precisely distinguishing physically realizable correlations from nonphysical ones.
An optical scheme for simulating nonlocality distillation is proposed in post-quantum regime. The nonlocal boxes are simulated by measurements on appropriately pre- and post-selected polarization entangled photon pairs, i.e. post-quantum nonlocality is simulated by exploiting fair-sampling loophole in a Bell test. Mod 2 addition on the outputs of two nonlocal boxes combined with pre- and post-selection operations constitutes the key operation of simulating nonlocality distillation. This scheme provides a possible tool for the experimental study on the nonlocality in post-quantum regime and the exact physical principle precisely distinguishing physically realizable correlations from nonphysical ones.
We report the first experimental demonstration of distillation of quantum nonlocality, confirming the recent theoretical protocol [Phys. Rev. Lett. 102, 120401 (2009)]. Quantum nonlocality is described by a correlation box with binary inputs and outputs, and the nonlocal boxes are realized through appropriate measurements on polarization entangled photon pairs. We demonstrate that nonlocality is amplified by connecting two nonlocal boxes into a composite one through local operations and four-photon measurements.
We first present a protocol for deterministically distilling nonlocality, building upon a recent result of Forster et al. [Phys. Rev. Lett. 102, 120401 (2009)10.1103/PhysRevLett.102.120401]. Our protocol, which is optimal for two-copy distillation, works efficiently for a specific class of postquantum nonlocal boxes, which we term correlated nonlocal boxes. In the asymptotic limit, all correlated nonlocal boxes are distilled to the maximally nonlocal box of Popescu and Rohrlich. Then, taking advantage of a result of Brassard et al. [Phys. Rev. Lett. 96, 250401 (2006)10.1103/PhysRevLett.96.250401] we show that all correlated nonlocal boxes make communication complexity trivial, and therefore appear very unlikely to exist in nature. Astonishingly, some of these nonlocal boxes are arbitrarily close to the set of classical correlations. This result therefore gives new insight to the problem of why quantum nonlocality is limited.
The hypothetical nonlocal box (NLB) proposed by Popescu and Rohrlich allows two spatially separated parties, Alice and Bob, to exhibit stronger than quantum correlations. If the generated correlations are weak, they can sometimes be distilled into a stronger correlation by repeated applications of the NLB. Motivated by the limited distillability of NLBs, we initiate here a study of the distillation of correlations for nonlocal boxes that output quantum states rather than classical bits (qNLBs). We propose a new protocol for distillation and show that it asymptotically distills a class of correlated quantum nonlocal boxes to the value [Formula: see text], whereas in contrast, the optimal non-adaptive parity protocol for classical nonlocal boxes asymptotically distills only to the value 3.0. We show that our protocol is an optimal non-adaptive protocol for 1, 2 and 3 qNLB copies by constructing a matching dual solution for the associated primal semidefinite program (SDP). We conclude that qNLBs are a stronger resource for nonlocality than NLBs. The main premise that develops from this conclusion is that the NLB model is not the strongest resource to investigate the fundamental principles that limit quantum nonlocality. As such, our work provides strong motivation to reconsider the status quo of the principles that are known to limit nonlocal correlations under the framework of qNLBs rather than NLBs.
The hypothetical nonlocal box (NLB) proposed by Popescu and Rohrlich allows two spatially sepa-rated parties, Alice and Bob, to exhibit stronger than quantum correlations. If the generated correlations are weak, they can sometimes be distilled into a stronger correlation by repeated applications of the NLB. Motivated by the limited distillability of NLBs, we initiate here a study of the distillation of correlations for nonlocal boxes that output quantum states rather than classical bits (qNLBs). We propose a new pro-tocol for distillation and show that it asymptotically distills a class of correlated quantum nonlocal boxes to the value 12 (3 3 + 1) ≈ 3.098076, whereas in contrast, the optimal non-adaptive parity protocol for classical nonlocal boxes asymptotically distills only to the value 3.0. We show that our protocol is an optimal non-adaptive protocol for 1, 2 and 3 qNLB copies by constructing a matching dual solution for the associated primal semidefinite program (SDP). We conclude that qNLBs are a stronger resource for nonlocality than NLBs. The main premise that develops from this conclusion is that the NLB model is not the strongest resource to investigate the fundamental principles that limit quantum nonlocality. As such, our work provides strong motivation to reconsider the status quo of the principles that are known
A set of nonlocal correlations that have come to be known as a Popescu-Rohrlich (PR) box suggest themselves as a natural unit of nonlocality, much as a singlet is a natural unit of entanglement. We present two results relevant to this idea. One is that a wide class of multipartite correlations can be simulated using local operations on PR boxes only. We show this with an explicit scheme, which has the interesting feature that the number of PR boxes required is related to the computational resources necessary to represent a function defining the multipartite box. The second result is that there are quantum multipartite correlations, arising from measurements on a cluster state, that cannot be simulated with n PR boxes, for any n.