Absolute separability witnesses for symmetric multiqubit states

Abstract

The persistent separability of certain quantum states, known as symmetric absolutely separable (SAS), under symmetry-preserving global unitary transformations is of key significance in the context of quantum resources for bosonic systems. In this work, we develop criteria for detecting SAS states of any number of qubits. Our approach is based on the Glauber-Sudarshan $P$ representation for finite-dimensional quantum systems. We introduce three families of SAS witnesses, one linear and two nonlinear in the eigenvalues of the state, formulated respectively as an algebraic inequality or a quadratic optimization problem. These witnesses are capable of identifying more SAS states than previously known counterparts. We also explore the geometric properties of the subsets of SAS states detected by our witnesses, shedding light on their distinctions.

arXiv comment16 pages, 5 figures

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Cited by in corpus (6)

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• 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
• On the extreme points of sets of absolulely separable and PPT states
• Detection of nonabsolute separability in quantum states and channels through moments