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Quantum Entropy and Its Use
I Entropies for Finite Quantum Systems.- 1 Fundamental Concepts.- 2 Postulates for Entropy and Relative Entropy.- 3 Convex Trace Functions.- II Entropies for General Quantum Systems.- 4 Modular
Quantum Information Theory and Quantum Statistics
Prerequisites from Quantum Mechanics.- Information and its Measures.- Entanglement.- More About Information Quantities.- Quantum Compression.- Channels and Their Capacity.- Hypothesis Testing.-
The semicircle law, free random variables, and entropy
Overview Probability laws and noncommutative random variables The free relation Analytic function theory and infinitely divisible laws Random matrices and asymptotically free relation Large
The proper formula for relative entropy and its asymptotics in quantum probability
Umegaki's relative entropyS(ω,ϕ)=TrDω(logDω−logDϕ) (of states ω and ϕ with density operatorsDω andDϕ, respectively) is shown to be an asymptotic exponent considered from the quantum hypothesis
Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality
We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality
Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
A subalgebraM0 of a von Neumann algebraM is called weakly sufficient with respect to a pair (φ,ω) of states if the relative entropy of φ and ω coincides with the relative entropy of their
Monotonicity of quantum relative entropy revisited
  • D. Petz
  • Mathematics, Physics
  • 6 September 2002
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