Skip to main content
SpringerLink
Log in

Some Aspects of Quantum Entanglement for CAR Systems

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

We show some distinct features of quantum entanglement for bipartite CAR systems such as the failure of triangle inequality of von Neumann entropy and the possible change of our entanglement degree under local operations. Those are due to the nonindependence of CAR systems and never occur in any algebraic independent systems. We introduce a new notion half-sided entanglement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Araki, H. and Lieb, E. H.: Entropy inequalities, Comm. Math. Phys. 18 (1970), 160–170.

    Google Scholar 

  2. Araki, H. and Moriya, H.: Equilibrium statistical mechanics of Fermion lattice systems, in preparation.

  3. Bennett, C. H., Di Vincenzo, D. P., Smolin, J. A. and Wootters, W. K.: Mixed-state entanglement and quantum error correction, Phys. Rev. A 54 (1996), 3824–3851.

    Google Scholar 

  4. Donald, M. J., Horodecki, M. and Rudolph, O.: The uniqueness theorem for entanglement measures, arXiv:quant-ph/0105017.

  5. Florig, M. and Summers, S. J.: On the statistical independence of algebras of observables, J. Math. Phys. 38 (1997), 1318–1328.

    Google Scholar 

  6. Haag, R. and Kastler, D.: An algebraic approach to quantum field theory, J. Math. Phys. 7 (1964), 848–861.

    Google Scholar 

  7. Horodecki, M., Horodecki, P. and Horodecki, R.: Limits for entanglement measures, Phys. Rev. Lett. 84 (2000), 2014–2017.

    Google Scholar 

  8. Lieb, E. H. and Ruskai, M. B.: Proof of the strong subadditivity of quantum-mechanical entropy, J. Math. Phys. 14 (1973), 1938–1941.

    Google Scholar 

  9. Narnhofer, H.: Entanglement for the Bose condensation, Phys. Lett. A 270 (2000), 232–238.

    Google Scholar 

  10. Rudolph, O.: A uniqueness theorem for entanglement measures, J. Math. Phys. 42 (2001), 2507–2512.

    Google Scholar 

  11. Summers, S. J.: On the independence of local algebras in quantum field theory, Rev. Math. Phys. 2 (1990), 201–247.

    Google Scholar 

  12. Takesaki, M.: Theory of Operator Algebras I, Springer, New York, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan

    Hajime Moriya

Authors
  1. Hajime Moriya
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moriya, H. Some Aspects of Quantum Entanglement for CAR Systems. Letters in Mathematical Physics 60, 109–121 (2002). https://doi.org/10.1023/A:1016158125660

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1016158125660

Search

Navigation