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…
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…
Quantum Information Theory and Quantum Statistics
- D. Petz
- Physics
- 3 December 2007
Prerequisites from Quantum Mechanics.- Information and its Measures.- Entanglement.- More About Information Quantities.- Quantum Compression.- Channels and Their Capacity.- Hypothesis Testing.-…
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…
Monotone metrics on matrix spaces
- D. Petz
- Mathematics, Computer Science
- 1 September 1996
Quasi-entropies for finite quantum systems
- D. Petz
- Physics
- 1 February 1986
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…
SUFFICIENCY OF CHANNELS OVER VON NEUMANN ALGEBRAS
- D. Petz
- Mathematics
- 1 March 1988
Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
- D. Petz
- Mathematics
- 1 March 1986
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…
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