Fidelity is a sub-martingale for discrete-time quantum filters
Quantum Physics
2016-11-17 v3 Optimization and Control
Abstract
Fidelity is known to increase through any Kraus map: the fidelity between two density matrices is less than the fidelity between their images via a Kraus map. We prove here that, in average, fidelity is also increasing for any discrete-time quantum filter: fidelity between the density matrix of the underlying Markov chain and the density matrix of its associated quantum filter is a sub-martingale. This result is not restricted to pure states. It also holds true for mixed states.
Cite
@article{arxiv.1005.3119,
title = {Fidelity is a sub-martingale for discrete-time quantum filters},
author = {Pierre Rouchon},
journal= {arXiv preprint arXiv:1005.3119},
year = {2016}
}