A sufficient condition for non-existence of symmetric extension of qudits using Bell inequalities

Meenu Kumari, Shohini Ghose, Robert B. Mann

Published 2017-04-21Version 1

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-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 CGLMP inequality is monogamous. Hence, the violation of the CGLMP inequality by any 2-qutrit state could be a sufficient condition for the non-existence of its symmetric extension.