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Quantum collapse rules from the maximum relative entropy principle
We show that the von Neumann–Luders collapse rules in quantum mechanics always select the unique state that maximises the quantum relative entropy with respect to the premeasurement state, subject toExpand
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W*-algebras and noncommutative integration
This text is a detailed overview of the theories of W*-algebras and noncommutative integration, up to the Falcone-Takesaki theory of noncommutative Lp spaces over arbitrary W*-algebras, and itsExpand
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The General Form of γ-Family of Quantum Relative Entropies
TLDR
We use the Falcone-Takesaki duality to extend the duality between coarse-grainings and Markov maps to the infinite-dimensional non-commutative case using the Legendre-Fenchel duality. Expand
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The general form of gamma-family of quantum relative entropies
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 naturallyExpand
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Local quantum information dynamics
In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description ofExpand
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Noncommutative Orlicz spaces over W*-algebras
Using the Falcone--Takesaki theory of noncommutative integration, we construct a family of noncommutative Orlicz spaces that are canonically associated to an arbitrary W*-algebra without any choiceExpand
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Lüders' and quantum Jeffrey's rules as entropic projections
TLDR
We prove that the standard quantum mechanical description of a quantum state change due to measurement, given by Luders’ rules, is a special case of the constrained maximisation of the quantum relative entropy functional. Expand
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Equivalence of tensor products over a category of W*-algebras
We prove the equivalence of two tensor products over a category of W*-algebras with normal (not necessarily unital) *-homomorphisms, defined by Guichardet and Dauns, respectively. This structureExpand
Quantum Schwarzschild space-time
Using new approach to construction of space-times emerging from quantum information theory, we identify the space of quantum states that generates the Schwarzschild space-time. No quantisationExpand
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Quantum Brègman distances and categories
TLDR
We introduce, and investigate the properties of, the family of quantum Br\`{e}gman distances, based on embeddings into suitable vector spaces (with the reflexive noncommutative Orlicz spaces over semi-finite W*-algebras providing two important examples). Expand