Quantum Correlations in Systems of Indistinguishable Particles

By K. Eckert, J. Schliemann, D. Bruß, Maciej Lewenstein. 2002

332 citations recorded by the source corpus.

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical investigations on quantum dots and neutral atoms in microtraps as tools for quantum information processing. We present analogies between distinguishable particles, bosons, and fermions in low-dimensional Hilbert spaces. We introduce the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles. This concept is generalized to mixed states and provides a correlation measure for indistinguishable particles. Then we generalize these notions to pure fermionic and bosonic states in higher-dimensional Hilbert spaces and also to the multi-particle case. We review the results on quantum correlations in mixed fermionic states and discuss the concept of fermionic Slater witnesses. Then the theory of quantum correlations in mixed bosonic states and of bosonic Slater witnesses is formulated. In both cases we provide methods of constructing optimal Slater witnesses that detect the degree of quantum correlations in mixed fermionic and bosonic states.

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

View Paper: https://www.semanticscholar.org/paper/ca463da9b804f9cb1799ac3d6ec8378200018b13

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum-enhanced measurements without entanglement (2017, background): “…instance, see (Amico et al., 2008; Balachandran et al., 2013; Banuls et al., 2006; Bloch et al., 2008; Calabrese et al., 2012; Dowling et al., 2006; Eckert et al., 2002; Ghirardi et al., 2002; Grabowski et al., 2011; Hines et al., 2003; Kraus et al., 2009; Lewenstein et al., 2007; Li et al., 2001;…”
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.”