Sufficient condition for nonexistence of symmetric extension of qudits using Bell inequalities

Sufficient condition for nonexistence of symmetric extension of qudits using Bell inequalities We analyze the connection between Bell inequality violations and symmetric extendibility of quantum states. We prove that 2-qubit reduced states of multiqubit symmetric pure states do not violate the Bell Clauser-Horne-Shimony-Holt (CHSH) inequality. We then prove the more general converse that any 2-qubit state that violates the CHSH inequality cannot have a symmetric extension. We extend our analysis to qudits and provide a test for symmetric extendibility of 2-qudit states. We show that if a 2-qudit Bell inequality is monogamous, then any 2-qudit state that violates this inequality does not have a symmetric extension. For the specific case of 2-qutrit states, we use numerical evidence to conjecture that the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality is monogamous. Hence, the violation of the CGLMP inequality by any 2-qutrit state could be a sufficient condition for the nonexistence of its symmetric extension. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Sufficient condition for nonexistence of symmetric extension of qudits using Bell inequalities

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Sufficient condition for nonexistence of symmetric extension of qudits using Bell inequalities

Abstract

We analyze the connection between Bell inequality violations and symmetric extendibility of quantum states. We prove that 2-qubit reduced states of multiqubit symmetric pure states do not violate the Bell Clauser-Horne-Shimony-Holt (CHSH) inequality. We then prove the more general converse that any 2-qubit state that violates the CHSH inequality cannot have a symmetric extension. We extend our analysis to qudits and provide a test for symmetric extendibility of 2-qudit states. We show that if a 2-qudit Bell inequality is monogamous, then any 2-qudit state that violates this inequality does not have a symmetric extension. For the specific case of 2-qutrit states, we use numerical evidence to conjecture that the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality is monogamous. Hence, the violation of the CGLMP inequality by any 2-qutrit state could be a sufficient condition for the nonexistence of its symmetric extension.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.012128
Publisher site
See Article on Publisher Site

Abstract

We analyze the connection between Bell inequality violations and symmetric extendibility of quantum states. We prove that 2-qubit reduced states of multiqubit symmetric pure states do not violate the Bell Clauser-Horne-Shimony-Holt (CHSH) inequality. We then prove the more general converse that any 2-qubit state that violates the CHSH inequality cannot have a symmetric extension. We extend our analysis to qudits and provide a test for symmetric extendibility of 2-qudit states. We show that if a 2-qudit Bell inequality is monogamous, then any 2-qudit state that violates this inequality does not have a symmetric extension. For the specific case of 2-qutrit states, we use numerical evidence to conjecture that the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality is monogamous. Hence, the violation of the CGLMP inequality by any 2-qutrit state could be a sufficient condition for the nonexistence of its symmetric extension.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jul 31, 2017

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