Monogamy of highly symmetric states

• URL: http://arxiv.org/abs/2309.16655v1
• Date: Thu, 28 Sep 2023 17:55:21 GMT
• Title: Monogamy of highly symmetric states
• Authors: Rene Allerstorfer and Matthias Christandl and Dmitry Grinko and Ion Nechita and Maris Ozols and Denis Rochette and Philip Verduyn Lunel
• Abstract summary: We study the question of how highly entangled two particles can be when also entangled in a similar way with other particles. In particular, we determine the exact maximum values of the projection to the maximally entangled state and antisymmetric Werner state possible.
• Score: 1.8323001213919563
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the question of how highly entangled two particles can be when also entangled in a similar way with other particles on the complete graph for the case of Werner, isotropic and Brauer states. In order to do so we solve optimization problems motivated by many-body physics, computational complexity and quantum cryptography. We formalize our question as a semi-definite program and then solve this optimization problem analytically, using tools from representation theory. In particular, we determine the exact maximum values of the projection to the maximally entangled state and antisymmetric Werner state possible, solving long-standing open problems. We find these optimal values by use of SDP duality and representation theory of the symmetric and orthogonal groups, and the Brauer algebra.

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