The automorphism group of separable states in quantum information theory

DOI10.1063/1.3578015zbMath1316.81014arXiv1012.4221OpenAlexW1965422276MaRDI QIDQ5263559

Yiu-Tung Poon, Nung-Sing Sze, Chi-Kwong Li, Shmuel Friedland

Publication date: 17 July 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.4221

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Quantum coherence, entanglement, quantum correlations (81P40) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (24)

Maps preserving transition probability from pure product states to pure states ⋮ Linear rank preservers of tensor products of rank one matrices ⋮ Linear maps preserving separability of pure states ⋮ Linear maps preserving determinant of tensor products of Hermitian matrices ⋮ Linear transformations between multipartite quantum systems that map the set of tensor product of idempotent matrices into idempotent matrix set ⋮ Preservers of restricted unitary orbits of projections ⋮ Linear maps preserving rank of tensor products of matrices ⋮ Linear preservers of tensor product of unitary orbits, and product numerical range ⋮ Linear maps on nonnegative symmetric matrices preserving the independence number ⋮ Unnamed Item ⋮ Entropy-preserving maps on quantum states ⋮ Linear maps preserving \(r\)-potents of tensor products of matrices ⋮ Linear maps preserving numerical radius of tensor products of matrices ⋮ Linear maps preserving idempotents of tensor products of matrices ⋮ Preservers of maximally entangled states ⋮ Linear rank one preservers on tensor products of Hermitian matrices ⋮ A note on classical adjoint commuting linear maps of tensor products of matrices ⋮ A note on linear preservers of certain ranks of tensor products of matrices ⋮ Characterizing operations preserving separability measures via linear preserver problems ⋮ A geometric characterization of quantum gates ⋮ Unnamed Item ⋮ On the preservers of maximally entangled states ⋮ LINEAR MAPS PRESERVING TENSOR PRODUCTS OF RANK-ONE HERMITIAN MATRICES ⋮ Commuting additive maps on tensor products of matrices

Cites Work

• Unnamed Item
• Product numerical range in a space with tensor product structure
• Separability of mixed states: necessary and sufficient conditions.
• Linear preservers on spaces of Hermitian or real symmetric matrices
• Unitarity as preservation of entropy and entanglement in quantum systems
• Quantum entanglement
• Characterizing operations preserving separability measures via linear preserver problems
• Classical deterministic complexity of Edmonds' Problem and quantum entanglement
• Separability Criterion for Density Matrices
• Unique decompositions, faces, and automorphisms of separable states
• An explicit expression for the relative entropy of entanglement in all dimensions
• Geometry of Quantum States
• Induced operators on symmetry classes of tensors

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