Symmetries in Exact Bohrification

Landsman, Klaas; Lindenhovius, Bert

doi:10.1007/978-981-13-2487-1_4

Cited by 2 publications

(2 citation statements)

References 35 publications

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“…Recall that for A = B(H A ) (in particular, for A = M n (C)) every such one-parameter group is given by conjugation with a unitary or anti-unitary operator by Wigner's theorem [7,64]. In fact, Wigner's theorem holds on the level of Jordan algebras [18,40]. In A, we obtain one-parameter groups of the form…”

Section: B Entanglement and Time Orientationsmentioning

confidence: 99%

Bipartite entanglement and the arrow of time

Frembs¹

2022

Preprint

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We provide a new perspective on the close relationship between entanglement and time. Our main focus is on bipartite entanglement, where this connection is foreshadowed both in the positive partial transpose criterion due to Peres [A. Peres, Phys. Rev. Lett., 77, 1413(1996] and in the classification of quantum within more general non-signalling bipartite correlations [M. Frembs and A. Döring, http://arxiv.org/abs/2204.11471]. Extracting the relevant common features, we identify a necessary and sufficient condition for bipartite entanglement in terms of a compatibility condition with respect to time orientations in local observable algebras, which express the dynamics in the respective subsystems. We discuss the relevance of the latter in the broader context of von Neumann algebras and the thermodynamical notion of time naturally arising within the latter.

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Section: B Entanglement and Time Orientationsmentioning

confidence: 99%

Bipartite entanglement and the arrow of time

Frembs¹

2022

Preprint

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“…This paper mainly concentrates on the Bohrification program in physics. For applications to mathematics see Döring & Harding (2010), Hamhalter (2011), Hamhalter & Turilova (2013), Wolters (2013), Döring (2014), Heunen (2014a,b), Lindenhovius, 2016), as well as the forthcoming review by Landsman & Lindenhovius (2016).…”

Section: Introductionmentioning

confidence: 99%

Bohrification: From classical concepts to commutative algebras

Landsman¹

2016

Preprint

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The Bohrification program is an attempt to interpret Bohr's mature doctrine of classical concepts as well as his earlier correspondence principle in the operator-algebraic formulation of quantum theory pioneered by von Neumann. In particular, this involves the study of commutative C*-algebras in relationship to noncommutative ones. This relationship may take the form of either exact Bohrification, in which one studies commutative unital C*-subalgebras of a given noncommutative C*-algebra, or asymptotic Bohrification, which involves deformations of commutative C*-algebras into noncommutative ones. Implementing the doctrine of classical concepts, exact Bohrification is an appropriate framework for the Kochen-Specker Theorem and for (intuitionistic) quantum logic, culminating in the topos-theoretic approach to quantum mechanics that has been developed since 1998. Asymptotic Bohrification was inspired by the correspondence principle and forms the right conceptual and mathematical framework for the explanation of the emergence of the classical world from quantum theory (incorporating the measurement problem and the closely related issue of spontaneous symmetry breaking). The Born rule may be derived from both exact and asymptotic Bohrification, which reflects the Janus faces of probability as applying to individual random events and to relative frequencies, respectively.We review the history, the goals, and the achievements of this program so far.

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Symmetries in Exact Bohrification

Cited by 2 publications

References 35 publications

Bipartite entanglement and the arrow of time

Bipartite entanglement and the arrow of time

Bohrification: From classical concepts to commutative algebras

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