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Separability gap and large-deviation entanglement criterion

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Jakub Czartowski, Konrad Szymański, Bartłomiej Gardas, Yan V. Fyodorov, Karol Zyczkowski

Original languageEnglish
Article number042326
JournalPhysical Review A
Issue number4
Published28 Oct 2019

King's Authors


For a given Hamiltonian H on a multipartite quantum system, one is interested in finding the energy E0 of its ground state. In the separability approximation, arising as a natural consequence of measurement in a separable basis, one looks for the minimal expectation value λmin- of H among all product states. For several concrete model Hamiltonians, we investigate the difference λmin - -E0, called the separability gap, which vanishes if the ground state has a product structure. In the generic case of a random Hermitian matrix of the Gaussian orthogonal ensemble, we find explicit bounds for the size of the gap which depend on the number of subsystems and hold with probability one. This implies an effective entanglement criterion applicable for any multipartite quantum system: If an expectation value of a typical observable of a given state is sufficiently distant from the average value, the state is almost surely entangled.

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