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arXiv · 1704.06516

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

Meenu Kumari·Shohini Ghose·Robert B. Mann
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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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Meenu Kumari, Shohini Ghose, Robert B. Mann. 2017-08-07. Sufficient condition for nonexistence of symmetric extension of qudits using Bell inequalities. https://doi.org/10.1103/physreva.96.012128

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