On duality between quantum maps and quantum states
Quantum Physics
2007-05-23 v1
Abstract
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations, determined by unitary matrices of extended dimensionality, is defined and analyzed. Using the concept of the dynamical matrix and the Jamiolkowski isomorphism we explore the relation between the set of quantum operations (dynamics) and the set of density matrices acting on an extended Hilbert space (kinematics). An analogous relation is established between the classical maps and an extended space of the discrete probability distributions.
Cite
@article{arxiv.quant-ph/0401119,
title = {On duality between quantum maps and quantum states},
author = {Karol Zyczkowski and Ingemar Bengtsson},
journal= {arXiv preprint arXiv:quant-ph/0401119},
year = {2007}
}
Comments
25 pages in revtex with 9 figures included