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- Ryszard Pawel Kostecki
- ArXiv
- 2014

We prove that the standard quantum mechanical description of a quantum state change due to measurement, given by Lüders’ rules, is a special case of the constrained maximisation of a quantum relative entropy functional. This result is a quantum analogue of the derivation of the Bayes–Laplace rule as a special case of the constrained maximisation of relative… (More)

- Ryszard Pawel Kostecki
- Open Syst. Inform. Dynam.
- 2011

We use the Falcone–Takesaki non-commutative flow of weights and the resulting theory of non-commutative Lp spaces in order to define the family of relative entropy functionals that naturally generalise the quantum relative entropies of Jenčová– Ojima and the classical relative entropies of Zhu–Rohwer, and belong to an intersection of families of Petz… (More)

We introduce, and investigate the properties of, the family of quantum Brègman distances, based on embeddings into suitable vector spaces (with the reflexive noncommutative Orlicz spaces over semi-finite W-algebras and noncommutative Lp spaces over any W-algebras providing two important examples). This allows us to define geometric categories for nonlinear… (More)

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