Infinitely entangled states
(pp281-306)
M. Keyl,
D. Schlingemann, and R.F. Werner
doi:
https://doi.org/10.26421/QIC3.4-1
Abstracts:
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.
Key words: infinitely
entangled states, infinite one-copy entanglement singular states, normal
states, C*-algebra, von Neumann algebra, maximally entangled states, EPR
states |