On the Contractivity of Hilbert-Schmidt distance under open system dynamics
Abstract
We show that the Hilbert-Schmidt distance, unlike the trace distance, between quantum states is generally not monotonic for open quantum systems subject to Lindblad semigroup dynamics. Sufficient conditions for contractivity of the Hilbert-Schmidt norm in terms of the dissipation generators are given. Although these conditions are not necessary, simulations suggest that non-contractivity is the typical case, i.e., that systems for which the Hilbert-Schmidt distance between quantum states is monotonically decreasing form only a small set of all possible dissipative systems for N>2, in contrast to the case N=2 where the Hilbert-Schmidt distance is always monotonically decreasing.
Keywords
Cite
@article{arxiv.0901.4547,
title = {On the Contractivity of Hilbert-Schmidt distance under open system dynamics},
author = {Xiaoting Wang and Sonia Schirmer},
journal= {arXiv preprint arXiv:0901.4547},
year = {2009}
}
Comments
Major revision. We would particularly like to thank D Perez-Garcia for constructive feedback