Entanglement marginal problems

• URL: http://arxiv.org/abs/2006.09064v5
• Date: Tue, 23 Nov 2021 07:04:48 GMT
• Title: Entanglement marginal problems
• Authors: Miguel Navascues, Flavio Baccari and Antonio Acin
• Abstract summary: entanglement marginal problem consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. We propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find that we can achieve an arbitrarily good approximation to the set of nearest-neighbour marginals of separable states with a time (space) complexity polynomial (linear) on the system size. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.

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