Positivity of linear maps under tensor powers

DOI10.1063/1.4927070zbMath1391.15108arXiv1502.05630OpenAlexW3099257677MaRDI QIDQ2786607

Alexander Müller-Hermes, David Reeb, Michael M. Wolf

Publication date: 15 February 2016

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

Full work available at URL: https://arxiv.org/abs/1502.05630

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) General theory of (C^*)-algebras (46L05) Positive linear operators and order-bounded operators (47B65) Multilinear algebra, tensor calculus (15A69) Channel models (including quantum) in information and communication theory (94A40) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items

Relative entropy bounds on quantum, private and repeater capacities, Halos and undecidability of tensor stable positive maps, Decomposability of linear maps under tensor powers, Spin polarization-scaling quantum maps and channels, Temperley-Lieb quantum channels, Annihilating entanglement between cones, When do composed maps become entanglement breaking?, Asymptotic analysis for \(O_N^+\)-Temperley-Lieb quantum channels, Absolutely separating quantum maps and channels, Positive tensor products of maps andn-tensor-stable positive qubit maps, Tensor products of quantum mappings, Decomposable Pauli diagonal maps and tensor squares of qubit maps, Multivariate trace inequalities, Monotonicity of the quantum relative entropy under positive maps, Geometric Rényi divergence and its applications in quantum channel capacities, Capacity estimates via comparison with TRO channels, Quantum mappings and characterization of entangled quantum states, Positive maps and trace polynomials from the symmetric group, Compositions and tensor products of linear maps between matrix algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unitary designs and codes
• Separability of mixed states: necessary and sufficient conditions.
• Everything you always wanted to know about LOCC (but were afraid to ask)
• Strong Converse Rates for Quantum Communication
• The Squashed Entanglement of a Quantum Channel
• Entanglement-annihilating and entanglement-breaking channels
• Capacities of Quantum Erasure Channels
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• A semidefinite program for distillable entanglement
• Additivity of the classical capacity of entanglement-breaking quantum channels
• Tensor powers of 2-positive maps
• Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel
• Entanglement Breaking Channels
• “Pretty Strong” Converse for the Quantum Capacity of Degradable Channels
• Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model