Quantitative Quantum Zeno and Strong Damping Limits in Strong Topology

TL;DR

This paper provides a unified, quantitative analysis of the quantum Zeno effect and strong damping in infinite-dimensional open quantum systems, deriving bounds on convergence speeds and applying them to photon loss channels.

Contribution

It introduces a unified framework for analyzing quantum Zeno and strong damping effects with explicit convergence bounds in infinite-dimensional systems.

Findings

Proves quantum Zeno and strong damping effects in infinite-dimensional systems.

Derives explicit bounds on convergence speeds for these effects.

Applies results to photon loss channels with concrete bounds.

Abstract

Frequent applications of a mixing quantum operation to a quantum system slow down its time evolution and eventually drive it into the invariant subspace of the named operation. We prove this phenomenon, the quantum Zeno effect, and its continuous variant, strong damping, in a unified way for infinite-dimensional open quantum systems, while merely demanding that the respective mixing convergence holds pointwise for all states. Both results are quantitative in the following sense: Given the speed of convergence for the mixing limits, we can derive bounds on the convergence speed for the corresponding quantum Zeno and strong damping limits. We apply our results to prove quantum Zeno and strong damping limits for the photon loss channel with an explicit bound on the convergence speed.