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Journal of Mathematical Physics / Volume 51 / Issue 6 / ARTICLES / Quantum Information and Computation

J. Math. Phys. 51, 062202 (2010); http://dx.doi.org/10.1063/1.3399807 (23 pages)

Separability of N-particle fermionic states for arbitrary partitions

Tsubasa Ichikawa1, Toshihiko Sasaki2, and Izumi Tsutsui2

1Research Center for Quantum Computing, Interdisciplinary Graduate School of Science and Engineering, Kinki University, 3-4-1 Kowakae, Higashi-Osaka, Osaka 577-8502, Japan
2Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan

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(Received 9 February 2010; accepted 26 March 2010; published online 8 June 2010)

We present a criterion of separability for arbitrary s partitions of N-particle fermionic pure states. We show that, despite the superficial nonfactorizability due to the antisymmetry required by the indistinguishability of the particles, the states which meet our criterion have factorizable correlations for a class of observables which are specified consistently with the states. The separable states and the associated class of observables share an orthogonal structure, whose nonuniqueness is found to be intrinsic to the multipartite separability and leads to the nontransitivity in the factorizability, in general. Our result generalizes the previous result obtained by Ghirardi et al. [J. Stat. Phys. 108, 49 (2002)] for the s = 2 and s = N case.

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. PROLEGOMENON
  3. ANTISYMMETRIC SPACES AND PARTITIONED OBSERVABLES
  4. ARBITRARY SEPARABILITY FOR N -PARTICLE ANTISYMMETRIC STATES
    1. Orthogonal structure in states and observables
    2. Factorization of correlations
    3. Criterion of separability and the complete set of properties
  5. IMPLICATIONS OF THE ORTHOGONAL STRUCTURES: EXAMPLES
    1. Nonuniqueness
    2. Nontransitivity
    3. Cluster decomposition property
  6. CONCLUSIONS AND DISCUSSIONS

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KEYWORDS and PACS

Keywords

fermion systems, quantum entanglement

PACS

  • 05.30.Fk

    Fermion systems and electron gas

  • 03.67.Mn

    Entanglement measures, witnesses, and other characterizations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3399807

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.
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    T. Ichikawa, T. Sasaki, and I. Tsutsui, Phys. Rev. A 79, 052307 (2009).


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