Algebraic Approach to Entanglement and Entropy

We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation space of the observable algebra, once a state is chosen. In this...

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Published in:arXiv.org
Main Authors: Balachandran, A P, Govindarajan, T R, de Queiroz, Amilcar R, Reyes-Lega, A F
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 06.02.2013
Subjects:
Algebra
Anomalies
Braid theory
Braiding
Entropy
Epistemology
Hilbert space
Quantum entanglement
Quantum mechanics
Quantum theory
Subsystems
ISSN:2331-8422
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Abstract We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation space of the observable algebra, once a state is chosen. In this approach, which is based on the Gelfand-Naimark-Segal construction, the study of subsystems becomes particularly clear. We explicitly show how the problems associated with partial trace for the study of entanglement of identical particles are readily overcome. In particular, a suitable entanglement measure is proposed, that can be applied to systems of particles obeying Fermi, Bose, para- and even braid group statistics. The generality of the method is also illustrated by the study of time evolution of subsystems emerging from restriction to subalgebras. Also, problems related to anomalies and quantum epistemology are discussed.
AbstractList We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation space of the observable algebra, once a state is chosen. In this approach, which is based on the Gelfand-Naimark-Segal construction, the study of subsystems becomes particularly clear. We explicitly show how the problems associated with partial trace for the study of entanglement of identical particles are readily overcome. In particular, a suitable entanglement measure is proposed, that can be applied to systems of particles obeying Fermi, Bose, para- and even braid group statistics. The generality of the method is also illustrated by the study of time evolution of subsystems emerging from restriction to subalgebras. Also, problems related to anomalies and quantum epistemology are discussed.
Author Govindarajan, T R
Balachandran, A P
de Queiroz, Amilcar R
Reyes-Lega, A F
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Snippet We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard...
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SubjectTerms Algebra
Anomalies
Braid theory
Braiding
Entropy
Epistemology
Hilbert space
Quantum entanglement
Quantum mechanics
Quantum theory
Subsystems
Title Algebraic Approach to Entanglement and Entropy
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