The automorphism group of separable states in quantum information theory

Abstract

We show that the linear group of automorphism of Hermitian matrices which preserves the set of separable states is generated by \emph{natural} automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each tensor factor, and interchanging two tensor factors of the same dimension. We apply our results to preservers of the product numerical range.

15 pages

References in corpus (9)

• Quantum entanglement
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• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement Measures and Purification Procedures
• Unique decompositions, faces, and automorphisms of separable states
• Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory
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Cited by in corpus (14)

• Characterizing Operations Preserving Separability Measures via Linear Preserver Problems
• Norms and Cones in the Theory of Quantum Entanglement
• Linear rank preservers of tensor products of rank one matrices
• Order indices and entanglement production in quantum systems
• A geometric characterization of invertible quantum measurement maps
• Entanglement production by statistical operators
• Quantum Operation of Affective Artificial Intelligence
• Von Neumann's information engine without the spectral theorem
• Linear maps preserving numerical radius of tensor product of matrices
• Linear maps preserving the higher numerical ranges of tensor product of matrices
• Linear maps preserving separability of pure states
• Linear preservers and quantum information science
• Discrimination of symmetric states in operational probabilistic theory
• On the Preservers of Maximally Entangled States