Details
| Original language | English |
|---|---|
| Pages (from-to) | 281-306 |
| Number of pages | 26 |
| Journal | Quant. Inform. Comput. |
| Volume | 3 |
| Issue number | 4 |
| Publication status | Published - 2003 |
Abstract
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In: Quant. Inform. Comput., Vol. 3, No. 4, 2003, p. 281-306.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Infinitely entangled states
AU - Keyl, M.
AU - Schlingemann, D.
AU - Werner, R. F.
PY - 2003
Y1 - 2003
N2 - 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.
AB - 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.
M3 - Article
VL - 3
SP - 281
EP - 306
JO - Quant. Inform. Comput.
JF - Quant. Inform. Comput.
IS - 4
ER -