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Quantum Correlations in Two-Fermion Systems

John Schliemann·J. Ignacio Cirac·Marek Kus·Maciej Lewenstein·Daniel Loss
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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 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 of 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 number for some states.

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John Schliemann, J. Ignacio Cirac, Marek Kus, Maciej Lewenstein, Daniel Loss. 2001-04-20. Quantum Correlations in Two-Fermion Systems. https://doi.org/10.1103/physreva.64.022303

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