Spectral Properties of Symmetric Quantum States and Symmetric Entanglement Witnesses

Abstract

We introduce and explore two questions concerning spectra of operators that are of interest in the theory of entanglement in symmetric (i.e., bosonic) quantum systems. First, we investigate the inverse eigenvalue problem for symmetric entanglement witnesses -- that is, we investigate what their possible spectra are. Second, we investigate the problem of characterizing which separable symmetric quantum states remain separable after conjugation by an arbitrary unitary acting on symmetric space -- that is, which states are separable in every orthonormal symmetric basis. Both of these questions have been investigated thoroughly in the non-symmetric setting, and we contrast the answers that we find with their non-symmetric counterparts.

23 pages, 2 figures

References in corpus (3)

• Entanglement detection
• Spectral properties of entanglement witnesses
• Entangled subspaces and generic local state discrimination with pre-shared entanglement

Cited by in corpus (7)

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• Symmetric quantum states: a review of recent progress
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• Absolutely $k$-Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix
• Nonequivalence between absolute separability and positive partial transposition in the symmetric subspace
• Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses
• Polytopes of Absolutely Wigner Bounded Spin States