Quantum correlations in two-fermion systems

By J. Schliemann, J. I. Cirac, M. Kuś, Maciej Lewenstein, Daniel Loss. 2000

321 citations recorded by the source corpus.

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 gi ve 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3954a2b5154986ddd7cae30917bf0dd8d3d2541a

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Entanglement in many-body systems (2007, background): “Normalized in order to range in the interval [0, 1] this has been called the Fermionic concurrence C[|ω〉] (Eckert et al., 2002; Schliemann et al., 2001a,b) C[|ω〉] = |〈 ω̃ |ω 〉| = 8|pf[ω]| (17) 9 where ω̃ := 12ε ijklω∗k,l has been termed the dual to ω.”
Quantum-enhanced measurements without entanglement (2017, background): “…Hines et al., 2003; Kraus et al., 2009; Lewenstein et al., 2007; Li et al., 2001; Micheli et al., 2003; Modi et al., 2012; Paskauskas and You, 2001; Schliemann et al., 2001; Schuch et al., 2004; Song et al., 2012; Tichy et al., 2013; Wiseman and Vaccaro, 2003; Y.Shi, 2004) and references therein.”