dorsal/arxiv
View SchemaBounds on entanglement in qudit subsystems
| Authors | Vivien M Kendon, Karol Zyczkowski, William J Munro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0203037 |
| URL | https://arxiv.org/abs/quant-ph/0203037 |
| DOI | 10.1103/PhysRevA.66.062310 |
| Journal | Phys. Rev. A 66, 062310 (2002) |
Abstract
The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterised by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the other N-m qudits. We examine the entanglement in the space of mixed states of m qudits. We show that for a typical pure state of N qudits, its subsystems smaller than N/3 qudits will have a positive partial transpose and hence are separable or bound entangled. Additionally, our numerical results show that the probability of finding entangled subsystems smaller than N/3 falls exponentially in the dimension of the Hilbert space. The bulk of pure state Hilbert space thus consists of highly entangled states with multipartite entanglement encompassing at least a third of the qudits in the pure state.
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"abstract": "The entanglement in a pure state of N qudits (d-dimensional distinguishable\nquantum particles) can be characterised by specifying how entangled its\nsubsystems are. A generally mixed subsystem of m qudits is obtained by tracing\nover the other N-m qudits. We examine the entanglement in the space of mixed\nstates of m qudits. We show that for a typical pure state of N qudits, its\nsubsystems smaller than N/3 qudits will have a positive partial transpose and\nhence are separable or bound entangled. Additionally, our numerical results\nshow that the probability of finding entangled subsystems smaller than N/3\nfalls exponentially in the dimension of the Hilbert space. The bulk of pure\nstate Hilbert space thus consists of highly entangled states with multipartite\nentanglement encompassing at least a third of the qudits in the pure state.",
"arxiv_id": "quant-ph/0203037",
"authors": [
"Vivien M Kendon",
"Karol Zyczkowski",
"William J Munro"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.062310",
"journal_ref": "Phys. Rev. A 66, 062310 (2002)",
"title": "Bounds on entanglement in qudit subsystems",
"url": "https://arxiv.org/abs/quant-ph/0203037"
},
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