Advertisement

Analytical Optimization of Local Quantum Operation and Classical Communication

Conference paper
Part of the Mathematics for Industry book series (MFI, volume 1)

Abstract

This manuscript treats the situation that a quantum state is prepared as an input and is manipulated by local quantum operations and classical communications (LOCC). We analytically optimize the LOCC. Optimizations with respect to LOCC frequently appear in theories of quantum communication and computation. However, this optimization problem is difficult, since we have to fix infinite number of parameters in order to identify the LOCC. In fact, there is no recipe for optimizing LOCC except for the case that the input state is a pure state, which is a special case of a quantum state. In this manuscript, we optimize the LOCC for non-pure input states. As a result, this analytical method enables us to solve a fundamental problem in the quantum communication theory. We think that our analysis will help us to make more general recipe to optimize LOCC.

Keywords

Quantum communication Analytical optimization Entanglement distillation Local operations and classical communication Post-selection 

References

  1. 1.
    Azuma, K.: Phys. Rev. A 85, 062309 (2012)CrossRefGoogle Scholar
  2. 2.
    Azuma, K., Kato, G.: Phys. Rev. A 85, 060303(R) (2012)CrossRefGoogle Scholar
  3. 3.
    Childress, L., et al.: Phys. Rev. Lett. 96, 070504 (2006)CrossRefGoogle Scholar
  4. 4.
    Gour, G.: Phys. Rev. A 71, 012318 (2005)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Horodecki, R., Horodecki, P., Horodecki, M.: K. Horodecki. Rev. Mod. Phys. 81, 865 (2009)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Lo, H.K., Popescu, S.: Phys. Rev. A 63, 022301 (2001)CrossRefGoogle Scholar
  7. 7.
    Munro, W.J., et al.: Phys. Rev. Lett. 101, 040502 (2008)CrossRefGoogle Scholar
  8. 8.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  9. 9.
    Streltsov, A., Kapermann, H.: D. Bru. New J. Phys. 12, 123004 (2010)CrossRefGoogle Scholar
  10. 10.
    van Look, P., et al.: Phys. Rev. Lett. 96, 240501 (2006)CrossRefGoogle Scholar
  11. 11.
    Vidal, E.: J. Mod. Opt. 47, 355 (2000)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.NTT Communication Science LaboratoriesAtsugi-shiJapan

Personalised recommendations