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Proof of the strong subadditivity of quantum‐mechanical entropy
We prove several theorems about quantum‐mechanical entropy, in particular, that it is strongly subadditive.
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Inequalities for quantum entropy: A review with conditions for equality
This article presents self-contained proofs of the strong subadditivity inequality for von Neumann’s quantum entropy, S(ρ), and some related inequalities for the quantum relative entropy, mostExpand
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Minimal entropy of states emerging from noisy quantum channels
TLDR
We consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive trace-preserving map. Expand
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Monotone Riemannian metrics and relative entropy on noncommutative probability spaces
We use the relative modular operator to define a generalized relative entropy for any convex operator function g on (0,∞) satisfying g(1)=0. We show that these convex operator functions can beExpand
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The χ2-divergence and mixing times of quantum Markov processes
We introduce quantum versions of the χ2-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approachExpand
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Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result
AbstractWe prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ12) − S(γ1)Expand
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Contractivity of positive and trace-preserving maps under Lp norms
We provide a complete picture of contractivity of trace preserving positive maps with respect to p-norms. We show that for p>1 contractivity holds in general if and only if the map is unital. WhenExpand
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A UNIFIED TREATMENT OF CONVEXITY OF RELATIVE ENTROPY AND RELATED TRACE FUNCTIONS, WITH CONDITIONS FOR EQUALITY
We consider a generalization of relative entropy derived from the Wigner–Yanase–Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the jointExpand
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A Fundamental Property of Quantum-Mechanical Entropy
There are some properties of entropy, such as concavity and subadditivity, that are known to hold (in classical and in quantum mechanics) irrespective of any assumptions on the detailed dynamics of aExpand
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BEYOND STRONG SUBADDITIVITY? IMPROVED BOUNDS ON THE CONTRACTION OF GENERALIZED RELATIVE ENTROPY
New bounds are given on the contraction of certain generalized forms of the relative entropy of two positive semi-definite operators under completely positive mappings. In addition, severalExpand
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