Three-qubit entanglement witnesses with the full spanning properties

Abstract

We construct three-qubit entanglement witnesses with the properties that all the partial transposes have the spanning properties. These witnesses determine faces for separable states whose interior lies in the interior of PPT states, and so they detect sets of PPT entangled states with nonempty interiors. These witnesses also detect all kinds of bi-separable pure product states. Our construction depends on the observation that multi-partite entanglement witnesses correspond to multi-linear maps which are positive.

10 pages, 2 figures

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• Entanglement detection
• Spectral conditions for positive maps
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Cited by in corpus (9)

• Positive maps and trace polynomials from the symmetric group
• Various notions of positivity for bi-linear maps and applications to tri-partite entanglement
• The role of phases in detecting three-qubit entanglement
• Separability of three qubit Greenberger-Horne-Zeilinger diagonal states
• There exist infinitely many kinds of partial separability/entanglement
• Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems
• State-witness contraction
• Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system
• Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor