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Acta Physica Sinica

Testing quantum nonlocality with high probability using quantum mixed state based on hardy-type paradox

Jin Liu, Bo Miao, Xin-Yan Jia, Dai-He Fan

Published Jan 1, 2019• 3 citations

Abstract

量子非局域关联是量子力学预言的重要现象, 同时也是量子理论区别于经典理论的重要特征之一. 因此, 对量子非局域关联的高成功概率检验有着重要意义. 本文提出了一种基于Hardy-type佯谬的、可用于针对纯态和混合态进行高成功概率量子非局域关联检验的逻辑, 并对其适用性进行了证明. 研究发现, 利用本文提出的检验逻辑对量子纯态进行量子非局域关联检验, 成功检验概率将随着量子纯态的纠缠度增加而出现先增大后减小的现象, 最大的成功检验概率超过39%. 进一步利用提出的检验逻辑, 以Werner态这种量子混合态为例, 进行了针对混合态的量子非局域关联的高概率检验研究. 研究发现, 随着混合态的纯度增加, 成功进行量子非局域关联检验的概率也将增加. 最后给出了针对Werner态这种量子混合态进行高成功概率量子非局域关联检验的条件和范围.

DOI: 10.7498/aps.68.20191125

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量子非局域关联是量子力学预言的重要现象, 同时也是量子理论区别于经典理论的重要特征之一. 因此, 对量子非局域关联的高成功概率检验有着重要意义. 本文提出了一种基于Hardy-type佯谬的、可用于针对纯态和混合态进行高成功概率量子非局域关联检验的逻辑, 并对其适用性进行了证明. 研究发现, 利用本文提出的检验逻辑对量子纯态进行量子非局域关联检验, 成功检验概率将随着量子纯态的纠缠度增加而出现先增大后减小的现象, 最大的成功检验概率超过39%. 进一步利用提出的检验逻辑, 以Werner态这种量子混合态为例, 进行了针对混合态的量子非局域关联的高概率检验研究. 研究发现, 随着混合态的纯度增加, 成功进行量子非局域关联检验的概率也将增加. 最后给出了针对Werner态这种量子混合态进行高成功概率量子非局域关联检验的条件和范围.

Bell nonlocality is a special quantum nonlocality and has emerged as an important resource in quantum information processing tasks. Typically, there are two types of strategies for testing the Bell nonlocality: the Bell inequality method and the “all-versus-nothing proof", the later includes methods such as the GHZ argument and Hardy paradox. The objective of this work is to provide new methods for detecting Bell nonlocality by understanding Hardy-like paradoxes (HLPs) and Hardy-Bell inequalities (HBIs) as well as Hardy inequality. First, the weak HLP (WHLP) is established, and an HBI is obtained for tripartite correlation tensors (CTs) with two inputs and two outcomes. Based on an existing Hardy inequality for an n-qubit pure state, a Hardy inequality is proven for n-partite Bell local CTs. Second, the WHLP and HBI are proven for tripartite states in terms of conditional probabilities. Our WHLP is theoretically and practically easier to construct and more efficient in checking Bell nonlocality compared to the usual HLP.

Characterizing high-dimensional entangled states is of crucial importance in quantum information science and technology. Recent theoretical progress has been made to extend Hardy's paradox into a general scenario with multisetting and multidimensional systems, which enables the maximum probability of nonlocal events to surpass the bound that was limited in Hardy's original test. Hitherto, no experimental verification has been conducted to verify Hardy's paradox, as most of the previous experimental efforts were restricted to two-dimensional systems. Here, based on two-photon high-dimensional orbital angular momentum (OAM) entanglement, we report an experiment to demonstrate Hardy's paradox for multiple settings and multiple outcomes. We demonstrate the paradox for two-setting higher-dimensional OAM subspaces up to

d=7

, which reveals that the nonlocal events increase with dimension. Furthermore, we showcase the nonlocality with an experimentally recorded probability of 36.77% for a five-setting three-dimensional OAM subspace via entanglement concentration, thus showing a sharper contradiction between quantum mechanics and classical theory.

The general Hardy-like quantum pigeonhole paradoxes for n-qubit states were presented by Tang [W. Tang, Phys. Rev. A 105, 032457 (2022)]. It has been shown that each of such paradoxes can be associated with an uncolorable solution of a specific vertex-coloring problem induced from the projected-coloring graph (a kind of unconventional graph). The Hardy-like quantum pigeonhole paradoxes can even give rise to a higher suc- cess probability in demonstrating the conflict between quantum mechanics and local or noncontextual realism than the previous Hardy's paradoxes. Moreover, multiqubit states and high-dimensional states can exhibit paradoxes. In contrast to only one type of contradiction presented in the original quantum pigeonhole paradox, we discussed two kinds of three-qubit projected-coloring graph states as the minimal illustration in our work. An optical experiment to verify such a stronger paradox is performed. This quantum paradox provides innovative thoughts and methods for exploring new types of stronger multiparty quantum nonlocality. It may have potential applications in untrusted multiparty communications and device-independent random number generation.