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Quantum Information Processing

Multipartite strongly symmetric states and applications to geometric entanglement and classicality

Liang Xiong, Qi Qin, Jianzhou Liu, Zhirui Gong, Zhan-Feng Jiang, Nung-Sing Sze

Published Jul 18, 2023• 0 citations
Publisher
DOI
10.1007/s11128-023-04032-y

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We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We give a highly intuitive geometric interpretation to entanglement via the Majorana representation, where these states correspond to points on a unit sphere. We use this to show how various entanglement properties are determined by the symmetry properties of the states. The geometric measure of entanglement is thus phrased entirely as a geometric optimization and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally, we see that different symmetries of the states correspond to different types of entanglement with respect to interconvertibility under stochastic local operations and classical communication.