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2003 | 1 | 2 | 289-306
Tytuł artykułu

Entanglement in the second quantization formalism

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca

Czasopismo
Rocznik
Tom
1
Numer
2
Strony
289-306
Opis fizyczny
Daty
wydano
2003-06-01
online
2003-06-01
Twórcy
  • Optics Section, The Blackett Laboratory, Imperial College, SW7 2BZ, London, UK, v.vedral@ic.ac.uk
Bibliografia
  • [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]
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  • [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.
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  • [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]
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  • [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]
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  • [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]
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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