Monotonicity of quantum relative entropy revisited

By Dénes Petz. 2002

193 citations recorded by the source corpus.

Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences such as the strong sub-additivity of the von Neumann entropy, the Golden-Thompson trace inequality and the monotonicity of the Holevo quantity.The relation to quantum Markovian states is briefly indicated.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b9fbe75500b33454dd49c1094749fb5e40c2e53c

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In Artificial Intelligence

In Statistical and Nonlinear Physics

Citations in the corpus

Quantum processes which do not use coherence (2015, background): “[49] Dénes Petz, “Monotonicity of quantum relative entropy revisited,” Reviews in Mathematical Physics 15, 79–91 (2003).”
Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions (2016, unknown): “[75] but is hard to translate physically.”
Monotonicity of the Quantum Relative Entropy Under Positive Maps (2015, background): “The question of monotonicity of the quantum relative entropy has however remained open [12, 30, 34, 36] for the natural class of linear maps Φ : T (H) → T (H′) that are subject only to the constraint that they map quantum states to quantum states.”
The classical-quantum boundary for correlations: Discord and related measures (2011, methodology): “Next they make use of Petz’s theorem (Petz, 2003), which says that I(ρ) = I(Γ(ρ)) if and only if the action of Γ can be inverted, i.e. there exists a Λ such that Λ(Γ(ρ)) = ρ. Putting it all together, they show that a state ρ can be locally broadcasted if and only if it is fully classically…”