Maps on states preserving the relative entropy

DOI10.1063/1.2898693zbMath1153.81407OpenAlexW2081359830MaRDI QIDQ3544654

Lajos Molnár

Publication date: 8 December 2008

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

Full work available at URL: http://hdl.handle.net/2437/81292

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Quantum equilibrium statistical mechanics (general) (82B10) Transformers, preservers (linear operators on spaces of linear operators) (47B49) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items (14)

Preservers for the Tsallis entropy of convex combinations of density operators ⋮ Maps on quantum states preserving Bregman and Jensen divergences ⋮ Maps on the positive definite cone of a \(C^\ast\)-algebra preserving certain quasi-entropies ⋮ Maps on density operators preserving quantum \(f\)-divergences ⋮ Characterizations of Jordan \(^*\)-isomorphisms of \(C^*\)-algebras by weighted geometric mean related operations and quantities ⋮ Maps on positive definite operators preserving the quantum \(\chi_\alpha ^2\)-divergence ⋮ \(\alpha\)-\(z\)-Rényi relative entropy related quantities and their preservers ⋮ Maps on positive operators preserving Rényi type relative entropies and maximal \(f\)-divergences ⋮ Order automorphisms on positive definite operators and a few applications ⋮ Entropy-preserving maps on quantum states ⋮ Transformations on density operators and on positive definite operators preserving the quantum Rényi divergence ⋮ Maps on states preserving the relative entropy. II ⋮ Maps preserving operator pairs whose products are projections ⋮ Isometries and relative entropy preserving maps on density operators

Cites Work

• Selected preserver problems on algebraic structures of linear operators and on function spaces
• The role of relative entropy in quantum information theory
• Isometries of quantum states
• Preserving the measure of compatibility between quantum states
• Fidelity preserving maps on density operators

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