dorsal/arxiv
View SchemaDescribing mixed spin-space entanglement of pure states of indistinguishable particles using an occupation number basis
| Authors | J. R. Gittings, A. J. Fisher |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202051 |
| URL | https://arxiv.org/abs/quant-ph/0202051 |
| DOI | 10.1103/PhysRevA.66.032305 |
| Journal | Phys. Rev. A 66, 032305 (2002) |
Abstract
Quantum mechanical entanglement is a resource for quantum computation, quantum teleportation, and quantum cryptography. The ability to quantify this resource correctly has thus become of great interest to those working in the field of quantum information theory. In this paper, we show that all existing entanglement measures but one fail important tests of fitness when applied to n particle, m site states of indistinguishable particles, where n,m>=2. The accepted method of measuring the entanglement of a bipartite system of distinguishable particles is to use the von Neumann entropy of the reduced density matrix of one half of the system. We show that expressing the full density matrix using a site-spin occupation number basis, and reducing with respect to that basis, gives an entanglement which meets all currently known fitness criteria for systems composed of either distinguishable or indistinguishable particles. We consider an output state from a previously published thought experiment, a state which is entangled in both spin and spatial degrees of freedom, and show that the site entropy measure gives the correct total entanglement. We also show how the spin-space entanglement transfer occurring within the apparatus can be understood in terms of the transfer of probability from single-occupancy to double-occupancy sectors of the density matrix.
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"abstract": "Quantum mechanical entanglement is a resource for quantum computation,\nquantum teleportation, and quantum cryptography. The ability to quantify this\nresource correctly has thus become of great interest to those working in the\nfield of quantum information theory. In this paper, we show that all existing\nentanglement measures but one fail important tests of fitness when applied to n\nparticle, m site states of indistinguishable particles, where n,m\u003e=2. The\naccepted method of measuring the entanglement of a bipartite system of\ndistinguishable particles is to use the von Neumann entropy of the reduced\ndensity matrix of one half of the system. We show that expressing the full\ndensity matrix using a site-spin occupation number basis, and reducing with\nrespect to that basis, gives an entanglement which meets all currently known\nfitness criteria for systems composed of either distinguishable or\nindistinguishable particles.\n We consider an output state from a previously published thought experiment, a\nstate which is entangled in both spin and spatial degrees of freedom, and show\nthat the site entropy measure gives the correct total entanglement. We also\nshow how the spin-space entanglement transfer occurring within the apparatus\ncan be understood in terms of the transfer of probability from single-occupancy\nto double-occupancy sectors of the density matrix.",
"arxiv_id": "quant-ph/0202051",
"authors": [
"J. R. Gittings",
"A. J. Fisher"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.032305",
"journal_ref": "Phys. Rev. A 66, 032305 (2002)",
"title": "Describing mixed spin-space entanglement of pure states of indistinguishable particles using an occupation number basis",
"url": "https://arxiv.org/abs/quant-ph/0202051"
},
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