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Title: General tradeoff relations of quantum nonlocality in the Clauser–Horne–Shimony–Holt scenario

Abstract

General tradeoff relations present in nonlocal correlations of bipartite systems are studied, regardless of any specific quantum states and measuring directions. Extensions to multipartite scenarios are possible and very promising. Tsirelson’s bound can be derived out in particular. The close connection with uncertainty relations is also presented and discussed. - Highlights: • Quantum violation of CHSH inequalities is found to satisfy tradeoff relations. • Tsirelson’s bound for quantum mechanics can be directly implied from these tradeoffs. • Tradeoff relations shed new light on uncertainty relations in summation forms.

Authors:
 [1];  [2];  [3];  [1]
  1. Department of Physics Education, Chonnam National University, Gwangju 500-757 (Korea, Republic of)
  2. Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China)
  3. (Singapore)
Publication Date:
OSTI Identifier:
22617471
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 377; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LOCALITY; QUANTUM MECHANICS; QUANTUM STATES

Citation Formats

Su, Hong-Yi, E-mail: hongyisu@chonnam.ac.kr, Chen, Jing-Ling, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, and Hwang, Won-Young, E-mail: wyhwang@jnu.ac.kr. General tradeoff relations of quantum nonlocality in the Clauser–Horne–Shimony–Holt scenario. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2016.12.035.
Su, Hong-Yi, E-mail: hongyisu@chonnam.ac.kr, Chen, Jing-Ling, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, & Hwang, Won-Young, E-mail: wyhwang@jnu.ac.kr. General tradeoff relations of quantum nonlocality in the Clauser–Horne–Shimony–Holt scenario. United States. doi:10.1016/J.AOP.2016.12.035.
Su, Hong-Yi, E-mail: hongyisu@chonnam.ac.kr, Chen, Jing-Ling, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, and Hwang, Won-Young, E-mail: wyhwang@jnu.ac.kr. Wed . "General tradeoff relations of quantum nonlocality in the Clauser–Horne–Shimony–Holt scenario". United States. doi:10.1016/J.AOP.2016.12.035.
@article{osti_22617471,
title = {General tradeoff relations of quantum nonlocality in the Clauser–Horne–Shimony–Holt scenario},
author = {Su, Hong-Yi, E-mail: hongyisu@chonnam.ac.kr and Chen, Jing-Ling and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 and Hwang, Won-Young, E-mail: wyhwang@jnu.ac.kr},
abstractNote = {General tradeoff relations present in nonlocal correlations of bipartite systems are studied, regardless of any specific quantum states and measuring directions. Extensions to multipartite scenarios are possible and very promising. Tsirelson’s bound can be derived out in particular. The close connection with uncertainty relations is also presented and discussed. - Highlights: • Quantum violation of CHSH inequalities is found to satisfy tradeoff relations. • Tsirelson’s bound for quantum mechanics can be directly implied from these tradeoffs. • Tradeoff relations shed new light on uncertainty relations in summation forms.},
doi = {10.1016/J.AOP.2016.12.035},
journal = {Annals of Physics},
number = ,
volume = 377,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2017},
month = {Wed Feb 15 00:00:00 EST 2017}
}
  • The Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality (in terms of correlation functions) of two qutrits is studied in detail by employing tritter measurements. A uniform formula for the maximum value of this inequality for tritter measurements is obtained. Based on this formula, we show that nonmaximally entangled states violate the BCHSH inequality more strongly than the maximally entangled one. This result is consistent with what was obtained by Acin et al. [Phys. Rev. A 65, 052325 (2002)] using the Bell-Clauser-Horne inequality (in terms of probabilities)
  • Clauser-Horne-Shimony-Holt inequality for bipartite systems of four dimensions is studied in detail by employing the unbiased eight-port beam splitters measurements. The uniform formulas for the maximum and minimum values of this inequality for such measurements are obtained. Based on these formulas, we show that an optimal nonmaximally entangled state is about 6% more resistant to noise than the maximally entangled one. We also give the optimal state and the optimal angles which are important for experimental realization.
  • Maximally entangled states should maximally violate the Bell inequality. It is proved that all two-qubit states that maximally violate the Bell-Clauser-Horne-Shimony-Holt inequality are exactly Bell states and the states obtained from them by local transformations. The proof is obtained by using the certain algebraic properties that Pauli's matrices satisfy. The argument is extended to the three-qubit system. Since all states obtained by local transformations of a maximally entangled state are equally valid entangled states, we thus give the characterizations of maximally entangled states in both the two-qubit and three-qubit systems in terms of the Bell inequality.
  • We characterize violation of Clauser-Horne-Shimony-Holt (CHSH) inequalities for mixed two-qubit states by their mixedness and entanglement. The class of states that have maximum degree of CHSH violation for a given linear entropy is also constructed.
  • We show that some two-party Bell inequalities with two-valued observables are stronger than the CHSH inequality for 3x3 isotropic states in the sense that they are violated by some isotropic states in the 3x3 system that do not violate the CHSH inequality. These Bell inequalities are obtained by applying triangular elimination to the list of known facet inequalities of the cut polytope on nine points. This gives a partial solution to an open problem posed by Collins and Gisin. The results of numerical optimization suggest that they are candidates for being stronger than the I{sub 3322} Bell inequality for 3x3more » isotropic states. On the other hand, we found no Bell inequalities stronger than the CHSH inequality for 2x2 isotropic states. In addition, we illustrate an inclusion relation among some Bell inequalities derived by triangular elimination.« less