Quantum correlations in two-fermion systems

John Schliemann, J. Ignacio Cirac, Marek Kuś, Maciej Lewenstein, and Daniel Loss
Phys. Rev. A 64, 022303 – Published 3 July 2001
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Abstract

We characterize and classify quantum correlations in two-fermion systems having 2K single-particle states. For pure states we introduce the Slater decomposition and rank (in analogy to Schmidt decomposition and rank); i.e., we decompose the state into a combination of elementary Slater determinants formed by pairs of mutually orthogonal single-particle states. Mixed states can be characterized by their Slater number which is the minimal Slater rank required to generate them. For K=2 we give a necessary and sufficient condition for a state to have a Slater number 1. We introduce a correlation measure for mixed states which can be evaluated analytically for K=2. For higher K, we provide a method of constructing and optimizing Slater number witnesses, i.e., operators that detect Slater numbers for some states.

  • Received 18 December 2000

DOI:https://doi.org/10.1103/PhysRevA.64.022303

©2001 American Physical Society

Authors & Affiliations

John Schliemann1, J. Ignacio Cirac2, Marek Kuś3, Maciej Lewenstein4, and Daniel Loss5

  • 1Department of Physics, The University of Texas, Austin, Texas 78712
  • 2Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
  • 3Centre for Theoretical Physics, Polish Academy of Sciences, 02668 Warsaw, Poland
  • 4Institut für Theoretische Physik, Universität Hannover, 30167 Hannover, Germany
  • 5Department of Physics and Astronomy, University of Basel, CH-4056 Basel, Switzerland

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Vol. 64, Iss. 2 — August 2001

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