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Journal of Mathematical Physics / Volume 53 / Issue 2 / ARTICLES / Quantum Information and Computation

J. Math. Phys. 53, 022202 (2012); http://dx.doi.org/10.1063/1.3685644 (8 pages)

Rank reduction for the local consistency problem

Jianxin Chen1,2, Zhengfeng Ji2,3, Alexander Klyachko4, David W. Kribs1,2, and Bei Zeng1,2

1Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario, Canada
2Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada
3State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China
4Department of Mathematics, Bilkent University, Bilkent, Ankara, Turkey

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(Received 2 September 2011; accepted 30 January 2012; published online 21 February 2012)

We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be compatible. We prove that any compatible local density operators can be satisfied by a low rank global density operator. Then we study both fermionic and bosonic versions of the N-representability problem as applications. After applying the channel-state duality, we prove that any compatible local channels can be obtained through a global quantum channel with small Kraus rank.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. PROOF OF MAIN THEOREM
  3. APPLICATION: N -REPRESENTABILITY PROBLEM
  4. LOCAL CONSISTENCY PROBLEM FOR QUANTUM CHANNELS
  5. SOME EXAMPLES
  6. CONCLUSION AND FUTURE WORKS

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KEYWORDS and PACS

Keywords

boson systems, fermion systems, quantum theory

PACS

  • 03.65.Ta

    Foundations of quantum mechanics; measurement theory

  • 05.30.Jp

    Boson systems

  • 05.30.Fk

    Fermion systems and electron gas

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3685644

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    Y.-K. Liu, M. Christandl, and F. Verstraete, Phys. Rev. Lett. 98, 110503 (2007).

    N. Linden and W. K. Wootters, Phys. Rev. Lett. 89, 277906 (2002).

    D. W. Smith, J. Chem. Phys. 43, S258 (1965)JCPSA600004300001000S258000001.

    N. S. Jones and N. Linden, Phys. Rev. A 71, 012324 (2005).

    D. Schlingemann and R. F. Werner, Phys. Rev. A 65, 012308 (2002).


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