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Open Physics

formerly Central European Journal of Physics


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2391-5471
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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

Published Online:
2003-06-01

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.

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

Keywords: 03.65.Ud; 71.10.Fd

  • [1] V. Vedral: “The role of relative entropy in quantum information theory”, Rev. Mod. Phys., Vol. 74, (2002), pp. 197–234. http://dx.doi.org/10.1103/RevModPhys.74.197 [Crossref]

  • [2] P. Zanardi: “Quantum entanglement in fermionic lattices”, Phys. Rev., Vol. A 65, (2002), pp. 042101. see also Y. Shi. “Quantum Entanglement of Identical Particles”, quant-ph/0205069, (2003) for a bosonic systems a similar argument was presented by S.J. van Enk, “Entanglement of photons”, Phys. Rev., vol. A 67, (2003), pp. 022303. http://dx.doi.org/10.1103/PhysRevA.65.042101 [Crossref]

  • [3] J. Schliemann, D. Loss, A.H. MacDonald: “Double-Occupancy Errors, Adiabaticity, and Entanglement of Spin-Qubits in Quantum Dots”, Phys. Rev., Vol. B 63, (2001), pp. 085311. J. Schliemann, J.I. Cirac, M. Kus, M. Lewenstein, D. Loss: “Quantum Correlations in Two-Fermion Systems”, Phys. Rev., Vol. A 64, (2001), pp. 022303. K. Eckert, J. Schliemann, D. Bruss, M. Lewenstein: “Quantum Correlations in Systems of Indistinguishable Particles”, Annals of Physics, Vol. 299, (2002), pp. 88–127. http://dx.doi.org/10.1103/PhysRevB.63.085311 [Crossref]

  • [4] S. Weinberg: The Quantum Theory of Fields, Cambridge University Press, Cambridge, 1997.

  • [5] D. Han, Y.S. Kim, M.E. Noz: “Illustrative example of Feynman's rest of the universe”, Am. J. Physics, Vol. 67 (1999), pp. 61–66. http://dx.doi.org/10.1119/1.19192 [Crossref]

  • [6] N.D. Birrell and P.C.W. Davies: Quantum Fields in Curved Space, Cambridge University Press, Cambridge, 1981.

  • [7] L. Mandel and E. Wolf: Optical Coherence and Quantum Optics, Cambridge University Press, Cambridge, 1995.

  • [8] E.. Lifshitz and L.P. Pitaevskii: Statistical Physics (Part Two), Pergamon Press, Oxford 1980.

  • [9] J.M. Vogels, K. Xu. Raman, J. R. Abo-Shaeer, W. Ketterle: “Experimental observation of the Bogoliubov transformation for a Bose-Einstein condensed gas”, Phys. Rev. Lett., Vol. 88, (2002), pp. 060402. http://dx.doi.org/10.1103/PhysRevLett.88.060402 [Crossref]

  • [10] S.A. Fulling: “Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time”, Phys. Rev., Vol. D 7, (1972), pp. 2850–2862.

  • [11] S.W. Hawking: “Black Hole Explosions?”, Nature, Vol. 248, (1974), pp. 30–31. http://dx.doi.org/10.1038/248030a0 [Crossref]

  • [12] L. Parker: “Quantized Fields and Particle Creation in Expanding Universes.I”, Phys. Rev., Vol. 183, (1969), pp. 1057–1067. http://dx.doi.org/10.1103/PhysRev.183.1057 [Crossref]

  • [13] M. Srednicki: “Entropy and area”, Phys. Rev. Lett., Vol. 71, (1993), pp. 666–669. http://dx.doi.org/10.1103/PhysRevLett.71.666 [Crossref]

  • [14] R. Wald: “The Thermodynamics of Black Holes”, Living Reviews of Relativity, (2001), can be found athttp://www.livingreviews.org.

  • [15] M. Horodecki, P. Horodecki, R. Horodecki: “Separability of mixed states: Necessary and sufficient conditions”, Phys. Lett. Vol. A 223, (1996), pp. 1–8. http://dx.doi.org/10.1016/S0375-9601(96)00706-2 [Crossref]

  • [16] W.K. Wootters: “Entanglement of formation of an arbitrary state of two qubits”, Phys. Rev. Lett., Vol.80, (1997), pp. 2245–2248. http://dx.doi.org/10.1103/PhysRevLett.80.2245 [Crossref]

  • [17] Y. Omar, N. Paunković, S. Bose, V. Vedral: “Spin-space entanglement transfer and quantum statistics”, Phys. Rev. Vol. A, (2002), pp. 062305. J.R. Gittings and A.J. Fisher: “Describing mixed spin-space entanglement of pure states of indistinguishable particles using an occupation-number basis”, Phys. Rev., Vol. A 66, (2002), pp. 032305. [Crossref]

  • [18] C.N. Yang: “Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors”, Rev. Mod. Phys., Vol. 34, (1962), pp. 694–704. http://dx.doi.org/10.1103/RevModPhys.34.694 [Crossref]

  • [19] T.D. Lee and C.N. Yang: “Many-Body Problem in Quantum Statistical Mechanics. I. General Formulation”, Phys. Rev., Vol. 113, (1959), pp. 1165–1177. http://dx.doi.org/10.1103/PhysRev.113.1165 [Crossref]

  • [20] N. Paunković, Y. Omar, S. Bose, V. Vedral: “Entanglement concentration using quantum statistics”, Phys. Rev. Lett. Vol. 88, (2002), pp. 187903. http://dx.doi.org/10.1103/PhysRevLett.88.187903 [Crossref]

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