Entanglement in the second quantization formalism |
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Authors: | Vlatko Vedral |
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Institution: | (1) Optics Section, The Blackett Laboratory, Imperial College, SW7 2BZ London, UK |
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Abstract: | 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. |
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Keywords: | entanglement many-particle systems quantum field theory particle statistics |
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