Entangled Rings
Quantum Physics
2009-11-06 v3 Condensed Matter
Abstract
Consider a ring of N qubits in a translationally invariant quantum state. We ask to what extent each pair of nearest neighbors can be entangled. Under certain assumptions about the form of the state, we find a formula for the maximum possible nearest-neighbor entanglement. We then compare this maximum with the entanglement achieved by the ground state of an antiferromagnetic ring consisting of an even number of spin-1/2 particles. We find that, though the antiferromagnetic ground state does not maximize the nearest-neighbor entanglement relative to all other states, it does so relative to other states having zero z-component of spin.
Cite
@article{arxiv.quant-ph/0009041,
title = {Entangled Rings},
author = {Kevin M. O'Connor and William K. Wootters},
journal= {arXiv preprint arXiv:quant-ph/0009041},
year = {2009}
}
Comments
19 pages, no figures; v2 includes new results; v3 corrects a numerical error for the case N=8