Quantum mechanics is nonlocal, which makes it different from classical mechanics. Quantum information and quantum computation is a promising frontier science which is based on quantum mechanics. The nonlocality of quantum mechanics is the fundamental reason that many quantum information processing tasks have significant advantages over their classical counterparts. In this dissertation, we study three aspects of quantum nonlocality, which include the quantitative relationship between entanglement and nonlocality, the quantification of genuine tripartite nonlocality and the distribution of nonlocal quantum resources. To be specific, • We investigate the quantitative relationship between entanglement and nonlocality of bipartite quantum systems. We start by exploiting the condition that the nonlocality of two different two-qubit states can be optimally examined by a same nonlocality test setting. Via numerical simulation, we find that the nonlocality of a generic two-qubit state is upper bounded by a function of the corresponding entanglement. Further, we give an analytical proof for the upper bound and find the class of two-qubit states that can reach the upper bound. • We analyze the quantification of genuine tripartite nonlocality of a generic three-qubit state. We find a method to solve the problem for a special class of three-qubit states which include not only pure states but also mixed states. Applying the method, we drive analytical results for the genuine tripartite nonlocality of generalized GHZ states, generalized Werner states and two class of mixed states with special correlation matrices. • We investigate the distribution of nonlocal quantum resources. To distribute bipartite nonlocal quantum resources, we design an efficient quantum repeater scheme, which not only achieves the optimal transmission rate but also consumes less resources of local operations and classical communication, for the case of general pure states of two-qubit system. We also analyze the case of bipartite pure states of arbitrary dimensional quantum system and get an upper bound on the probability of a successful projection operation to produce a maximally nonlocal state. To distribute tripartite nonlocal resources, we propose a simple scenario to generate tripartite nonlocal resources from bipartite nonlocal resources. As examples, we examine the cases that two-qubit Werner states and general two-qubit pure states are prepared as resources, respectively. We get the upper bounds on the genuine tripartite nonlocality that can be generated in the scenario. We also provide the optimal measurement settings to achieve the upper bounds.Quantum mechanics is nonlocal, which makes it different from classical mechanics. Quantum information and quantum computation is a promising frontier science which is based on quantum mechanics. The nonlocality of quantum mechanics is the fundamental reason that many quantum information processing tasks have significant advantages over their classical counterparts. In this dissertation, we study three aspects of quantum nonlocality, which include the quantitative relationship between entanglement and nonlocality, the quantification of genuine tripartite nonlocality and the distribution of nonlocal quantum resources. To be specific, • We investigate the quantitative relationship between entanglement and nonlocality of bipartite quantum systems. We start by exploiting the condition that the nonlocality of two different two-qubit states can be optimally examined by a same nonlocality test setting. Via numerical simulation, we find that the nonlocality of a generic two-qubit state is upper bounded by a function of the corresponding entanglement. Further, we give an analytical proof for the upper bound and find the class of two-qubit states that can reach the upper bound. • We analyze the quantification of genuine tripartite nonlocality of a generic three-qubit state. We find a method to solve the problem for a special class of three-qubit states which include not only pure states but also mixed states. Applying the method, we drive analytical results for the genuine tripartite nonlocality of generalized GHZ states, generalized Werner states and two class of mixed states with special correlation matrices. • We investigate the distribution of nonlocal quantum resources. To distribute bipartite nonlocal quantum resources, we design an efficient quantum repeater scheme, which not only achieves the optimal transmission rate but also consumes less resources of local operations and classical communication, for the case of general pure states of two-qubit system. We also analyze the case of bipartite pure states of arbitrary dimensional quantum system and get an upper bound on the probability of a successful projection operation to produce a maximally nonlocal state. To distribute tripartite nonlocal resources, we propose a simple scenario to generate tripartite nonlocal resources from bipartite nonlocal resources. As examples, we examine the cases that two-qubit Werner states and general two-qubit pure states are prepared as resources, respectively. We get the upper bounds on the genuine tripartite nonlocality that can be generated in the scenario. We also provide the optimal measurement settings to achieve the upper bounds.

Jan 1, 20180 citations

Revealing hidden standard tripartite nonlocality by local filtering

Qiao-Qiao Lv, Jin‐Min Liang, Zhi‐Xi Wang +1 more

arXiv:2205.10562Quantum Information ProcessingMay 1, 20221 citation

Experimental Demonstration of Genuine Tripartite Nonlocality under Strict Locality Conditions

Liang Huang, Xuemei Gu, Yang-Fan Jiang +9 more

Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevant events and employing fast quantum random number generators and high-speed polarization measurements. In particular, for a photonic quantum triangular network we observe a locality-loophole-free violation of the Bell-type inequality by 7.57 standard deviations for a postselected tripartite Greenberger-Horne-Zeilinger state of fidelity (93.13±0.24)%, which convincingly disproves the possibility of simulating genuine tripartite nonlocality by bipartite nonlocal resources with globally shared randomness.Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevant events and employing fast quantum random number generators and high-speed polarization measurements. In particular, for a photonic quantum triangular network we observe a locality-loophole-free violation of the Bell-type inequality by 7.57 standard deviations for a postselected tripartite Greenberger-Horne-Zeilinger state of fidelity (93.13±0.24)%, which convincingly disproves the possibility of simulating genuine tripartite nonlocality by bipartite nonlocal resources with globally shared randomness.

arXiv:2203.00889Physical Review LettersAug 2, 202215 citations

A Combinatorial Approach to Nonlocality and Contextuality

Antonio Acín, Tobias Fritz, Anthony Leverrier +1 more

arXiv:1212.4084Communications in Mathematical PhysicsJan 28, 2015182 citations

Construction of Sets of Orthogonal Quantum States with Minimal Nonlocality in Bipartite and Tripartite Systems of Unequal Local Dimensions

Ben-Hao Zhao, Dong-Huan Jiang, Yu-Guang Yang +1 more

The research on minimal nonlocality aims to determine the minimal cardinality of nonlocal sets of quantum states. However, the construction of a nonlocal set of states in bipartite or tripartite quantum systems with unequal local dimensions remains unsolved. In this paper, we first give a method to construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb{C}^{4} \otimes \mathbb{C}^{7}$ quantum system. Then we give a general method to construct a set of orthogonal quantum states with minimal nonlocality in a bipartite quantum system with unequal local dimensions. Furthermore, we generalize the construction method to tripartite quantum system with unequal local dimensions, and construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb C^{d_1} \otimes \mathbb C^{d_2}\otimes \mathbb C^{d_3}$ quantum system for $5\le d_1 < d_2 < d_3$ . Our work settles the construction problem of a set of orthogonal states with minimal nonlocality in both bipartite and tripartite systems with unequal local dimensions.The research on minimal nonlocality aims to determine the minimal cardinality of nonlocal sets of quantum states. However, the construction of a nonlocal set of states in bipartite or tripartite quantum systems with unequal local dimensions remains unsolved. In this paper, we first give a method to construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb{C}^{4} \otimes \mathbb{C}^{7}$ quantum system. Then we give a general method to construct a set of orthogonal quantum states with minimal nonlocality in a bipartite quantum system with unequal local dimensions. Furthermore, we generalize the construction method to tripartite quantum system with unequal local dimensions, and construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb C^{d_1} \otimes \mathbb C^{d_2}\otimes \mathbb C^{d_3}$ quantum system for $5\le d_1 < d_2 < d_3$. Our work settles the construction problem of a set of orthogonal states with minimal nonlocality in both bipartite and tripartite systems with unequal local dimensions.

quant-pharXiv:2607.28998Aug 3, 20260 citations

\mathbb{C}^{4} \otimes \mathbb{C}^{7}

quantum system. Then we give a general method to construct a set of orthogonal quantum states with minimal nonlocality in a bipartite quantum system with unequal local dimensions. Furthermore, we generalize the construction method to tripartite quantum system with unequal local dimensions, and construct a set of orthogonal quantum states with minimal nonlocality in

\mathbb C^{d_1} \otimes \mathbb C^{d_2}\otimes \mathbb C^{d_3}

quantum system for

5\le d_1 < d_2 < d_3

. Our work settles the construction problem of a set of orthogonal states with minimal nonlocality in both bipartite and tripartite systems with unequal local dimensions.