dorsal/arxiv
View SchemaOn the quantification of entanglement in infinite-dimensional quantum systems
| Authors | Jens Eisert, Christoph Simon, Martin B. Plenio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112064 |
| URL | https://arxiv.org/abs/quant-ph/0112064 |
| DOI | 10.1088/0305-4470/35/17/307 |
| Journal | Journal of Physics A 35, 3911 (2002) |
Abstract
We investigate entanglement measures in the infinite-dimensional regime. First, we discuss the peculiarities that may occur if the Hilbert space of a bi-partite system is infinite-dimensional, most notably the fact that the set of states with infinite entropy of entanglement is trace-norm dense in state space, implying that in any neighborhood of every product state there lies an arbitrarily strongly entangled state. The starting point for a clarification of this counterintuitive property is the observation that if one imposes the natural and physically reasonable constraint that the mean energy is bounded from above, then the entropy of entanglement becomes a trace-norm continuous functional. The considerations will then be extended to the asymptotic limit, and we will prove some asymptotic continuity properties. We proceed by investigating the entanglement of formation and the relative entropy of entanglement in the infinite-dimensional setting. Finally, we show that the set of entangled states is still trace-norm dense in state space, even under the constraint of a finite mean energy.
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"abstract": "We investigate entanglement measures in the infinite-dimensional regime.\nFirst, we discuss the peculiarities that may occur if the Hilbert space of a\nbi-partite system is infinite-dimensional, most notably the fact that the set\nof states with infinite entropy of entanglement is trace-norm dense in state\nspace, implying that in any neighborhood of every product state there lies an\narbitrarily strongly entangled state. The starting point for a clarification of\nthis counterintuitive property is the observation that if one imposes the\nnatural and physically reasonable constraint that the mean energy is bounded\nfrom above, then the entropy of entanglement becomes a trace-norm continuous\nfunctional. The considerations will then be extended to the asymptotic limit,\nand we will prove some asymptotic continuity properties. We proceed by\ninvestigating the entanglement of formation and the relative entropy of\nentanglement in the infinite-dimensional setting. Finally, we show that the set\nof entangled states is still trace-norm dense in state space, even under the\nconstraint of a finite mean energy.",
"arxiv_id": "quant-ph/0112064",
"authors": [
"Jens Eisert",
"Christoph Simon",
"Martin B. Plenio"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/35/17/307",
"journal_ref": "Journal of Physics A 35, 3911 (2002)",
"title": "On the quantification of entanglement in infinite-dimensional quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0112064"
},
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