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Open Physics

formerly Central European Journal of Physics

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Entanglement in the second quantization formalism

1Optics Section, The Blackett Laboratory, Imperial College, SW7 2BZ, London, UK

© 2003 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Open Physics. Volume 1, Issue 2, Pages 289–306, ISSN (Online) 2391-5471, DOI: 10.2478/BF02476298, June 2003

Publication History

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We study properties of entangled systems in the (mainly non-relativistic) second quantization formalism. This is then applied to interacting and non-interacting bosons and fermions and the differences between the two are discussed. We present a general formalism to show how entanglement changes with the change of modes of the system. This is illustrated with examples such as the Bose condensation and the Unruh effect. It is then shown that a non-interacting collection of fermions at zero temperature can be entangled in spin, providing that their distances do not exceed the inverse Fermi wavenumber. Beyond this distance all bipartite entanglement vanishes, although classical correlations still persist. We compute the entanglement of formation as well as the mutual information for two spin-correlated electrons as a function of their distance. The analogous, non-interacting collection of bosons displays no entanglement in the internal degrees of freedom. We show how to generalize our analysis of the entanglement in the internal degrees of freedom to an arbitrary number of particles.

Keywords: entanglement; many-particle systems; quantum field theory; particle statistics

Keywords: 03.65.Ud; 71.10.Fd

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