dorsal/arxiv
View SchemaInfinitely entangled states
| Authors | M. Keyl, D. Schlingemann, R. F. Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212014 |
| URL | https://arxiv.org/abs/quant-ph/0212014 |
Abstract
For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as a resource for tasks like the teleportation of arbitrarily many qubits. We show that appropriate states cannot be obtained by density operators in an infinite dimensional Hilbert space. However, using techniques for the description of infinitely many degrees of freedom from field theory and statistical mechanics, such states can nevertheless be constructed rigorously. We explore two related possibilities, namely an extended notion of algebras of observables, and the use of singular states on the algebra of bounded operators. As applications we construct the essentially unique infinite analogue of maximally entangled states, and the singular state used heuristically in the fundamental paper of Einstein, Rosen and Podolsky.
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"abstract": "For states in infinite dimensional Hilbert spaces entanglement quantities\nlike the entanglement of distillation can become infinite. This leads naturally\nto the question, whether one system in such an infinitely entangled state can\nserve as a resource for tasks like the teleportation of arbitrarily many\nqubits. We show that appropriate states cannot be obtained by density operators\nin an infinite dimensional Hilbert space. However, using techniques for the\ndescription of infinitely many degrees of freedom from field theory and\nstatistical mechanics, such states can nevertheless be constructed rigorously.\nWe explore two related possibilities, namely an extended notion of algebras of\nobservables, and the use of singular states on the algebra of bounded\noperators. As applications we construct the essentially unique infinite\nanalogue of maximally entangled states, and the singular state used\nheuristically in the fundamental paper of Einstein, Rosen and Podolsky.",
"arxiv_id": "quant-ph/0212014",
"authors": [
"M. Keyl",
"D. Schlingemann",
"R. F. Werner"
],
"categories": [
"quant-ph"
],
"title": "Infinitely entangled states",
"url": "https://arxiv.org/abs/quant-ph/0212014"
},
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