dorsal/arxiv
View SchemaQuantum Correlations in Systems of Indistinguishable Particles
| Authors | K. Eckert, J. Schliemann, D. Bruss, M. Lewenstein |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0203060 |
| URL | https://arxiv.org/abs/quant-ph/0203060 |
| DOI | 10.1006/aphy.2002.6268 |
| Journal | Annals of Physics 299 (2002), 88-127 |
Abstract
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.
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"abstract": "We discuss quantum correlations in systems of indistinguishable particles in\nrelation to entanglement in composite quantum systems consisting of well\nseparated subsystems. Our studies are motivated by recent experiments and\ntheoretical investigations on quantum dots and neutral atoms in microtraps as\ntools for quantum information processing. We present analogies between\ndistinguishable particles, bosons and fermions in low-dimensional Hilbert\nspaces. We introduce the notion of Slater rank for pure states of pairs of\nfermions and bosons in analogy to the Schmidt rank for pairs of distinguishable\nparticles. This concept is generalized to mixed states and provides a\ncorrelation measure for indistinguishable particles. Then we generalize these\nnotions to pure fermionic and bosonic states in higher-dimensional Hilbert\nspaces and also to the multi-particle case. We review the results on quantum\ncorrelations in mixed fermionic states and discuss the concept of fermionic\nSlater witnesses. Then the theory of quantum correlations in mixed bosonic\nstates and of bosonic Slater witnesses is formulated. In both cases we provide\nmethods of constructing optimal Slater witnesses that detect the degree of\nquantum correlations in mixed fermionic and bosonic states.",
"arxiv_id": "quant-ph/0203060",
"authors": [
"K. Eckert",
"J. Schliemann",
"D. Bruss",
"M. Lewenstein"
],
"categories": [
"quant-ph",
"cond-mat"
],
"doi": "10.1006/aphy.2002.6268",
"journal_ref": "Annals of Physics 299 (2002), 88-127",
"title": "Quantum Correlations in Systems of Indistinguishable Particles",
"url": "https://arxiv.org/abs/quant-ph/0203060"
},
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