Bounds on entanglement in qudit subsystems
Abstract
The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterised by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the other N-m qudits. We examine the entanglement in the space of mixed states of m qudits. We show that for a typical pure state of N qudits, its subsystems smaller than N/3 qudits will have a positive partial transpose and hence are separable or bound entangled. Additionally, our numerical results show that the probability of finding entangled subsystems smaller than N/3 falls exponentially in the dimension of the Hilbert space. The bulk of pure state Hilbert space thus consists of highly entangled states with multipartite entanglement encompassing at least a third of the qudits in the pure state.
Cite
@article{arxiv.quant-ph/0203037,
title = {Bounds on entanglement in qudit subsystems},
author = {Vivien M Kendon and Karol Zyczkowski and William J Munro},
journal= {arXiv preprint arXiv:quant-ph/0203037},
year = {2009}
}
Comments
7 pages, 3 embedded eps figures. v2 is restructured, one fig replaced, improved explanations, references updated; main results unchanged. v3 is minor improvements in line with referee comments, one ref and appendix added