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Quantum Optics$
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John Garrison and Raymond Chiao

Print publication date: 2008

Print ISBN-13: 9780198508861

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780198508861.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 18 October 2021

Entangled states

Entangled states

(p.193) 6 Entangled states
Quantum Optics

J. C. Garrison

R. Y. Chiao

Oxford University Press

A state of two distinguishable particles is “separable” if the wavefunction is a product of single-particle wavefunctions. Schrödinger introduced the term “entangled” to describe a two-particle state that is not separable. This notion is extended to all pairs of distinguishable quantum systems by using tensor products of Hilbert spaces and the Schmidt decomposition. Equivalent operational definitions are expressed in terms of correlation functions representing measurements. A state of two indistinguishable particles is kinematically separable if the product function satisfies Bose or Fermi statistics, otherwise it is kinematically entangled. Alternatively, a two-particle state is dynamically separable if the wavefunction has the minimal form required by Bose or Fermi statistics, and dynamically entangled otherwise. For photons, the role of the missing position-space wave function is played by a detection amplitude directly related to counting rates.

Keywords:   tensor product, reduced density operator, Schmidt decomposition, kinematically entangled, dynamically entangled, detection amplitude

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