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John Vaccaro

accessible. The entanglement of indistinguishable particles shared between two parties. Howard Wiseman. Griffith University, Brisbane, Australia. John Vaccaro. University of Hertfordshire, Hatfield, UK. Introduction. Pure states. where. Mixed states – open problem for dim > 2.

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John Vaccaro

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  1. accessible The entanglement of indistinguishable particles shared between two parties Howard Wiseman Griffith University, Brisbane, Australia John Vaccaro University of Hertfordshire, Hatfield, UK

  2. Introduction Pure states where Mixed states– open problem for dim > 2 Here:identical particles ? Contents Previous concepts • Entanglement of modes • Quantum correlations (QC) New measure Examples

  3. Previous concept - Entanglement of modes Zanardi, Wang Phys. Rev. A 65, 042101 (2002); J. Phys. A, 35 7947 (2002). Field modes have different occupation states Use Fock-state representation: take trace in Fock-state basis Example: for the single-particle state This concept underlies Tan, Walls & Collett single particle nonlocality [PRL 66, 252 (1991)] No notion of local particle number conservation

  4. Previous concept - “Quantum Correlations” (QC) Paskauskas & You PRA A 64, 042310 (2001). Schliemann, Cirac, Kus, Lewenstein & Loss PRA 64, 022303 (2001) Li, Zeng, Liu & Long PRA 64, 054302 (2001) Idea:isolate the symmetrization from entanglement - determine number of Slater determinants/permanents Most reduced form: Fermions Bosons

  5. Shannon entropy Given general 2-particle state: linear mode transfm: Examples: Fermions QC=0 Bosons QC=1 Bosons No notion of bi-partite separation

  6. New measure EP quant-ph/0210002 (to appear in PRL) Motivation: • LO can not increase entanglement • so transfer state to local registers using LO • particle number conservation implies local operations local particle number transfer first, last first, transfer last thus, entanglement is invariant to localparticle-number measurements

  7. Definition: projects onto n particles at A and N-n particles at B normalization * * The projection produces a mixture of states of definite particle number The projection eliminates coherences between states of different particle number Implements particle number conservation and preserves bi-partite separation

  8. Examples exactly 1 particle at each of A and B project onto states on definite particle number at A and B 0 particles at A E=0 1 particle at A E=0

  9. E=0 E=1 E=0

  10. Properties Super-additivity: Asymptotic limit: thus

  11. Comparisons

  12. Application 2 mode BEC c.f. Hines et al.PRA 67, 013609 (2003) (mode entanglement) But this is not accessible for transfer to local registers – not a resource

  13. SSR’s generally EP ignores coherence between subspaces of different local atom number. Effectively a superselection rule. Other local constraints or symmetries have similar effect  generalize into entanglement under SSR’s S.D.Bartlett, H.M. Wiseman, quant-ph/0303140

  14. indistinguishability introduces new features into QIT resources operationally motivateddefinition (entanglement as resource) super additiveproperty new study of entanglement in presence of SSR Summary

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