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We use the Falcone–Takesaki non-commutative flow of weights and the resulting theory of non-commutative L p 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 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)

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