Remark on multi-particle observables and entangled states with constant complexity
Quantum Physics
2007-05-23 v1
Abstract
We show that every density matrix of an n-particle system prepared by a quantum network of constant depth is asymptotically commuting with the mean-field observables. We introduce certain pairs of hypersurfaces in the space of density matrices and give lower bounds for the depth of a network which prepares states lying outside those pairs. The measurement of an observable which is not asymptotically commuting with the mean-field observables requires a network of depth in the order of log n, if one demands the measurement to project the state into the eigenspace of the measured observable.
Cite
@article{arxiv.quant-ph/0003117,
title = {Remark on multi-particle observables and entangled states with constant complexity},
author = {Dominik Janzing and Thomas Beth},
journal= {arXiv preprint arXiv:quant-ph/0003117},
year = {2007}
}
Comments
7 pages, Revtex