Quantum Zeno effect for open quantum systems

TL;DR

This paper extends the quantum Zeno effect to open quantum systems with unbounded generators and weaker assumptions on quantum operations, broadening the understanding of how frequent interventions can inhibit quantum evolution.

Contribution

It proves the quantum Zeno effect under weaker conditions, including unbounded generators and strong power-convergence, expanding the theoretical framework for open quantum systems.

Findings

Established quantum Zeno limit for unbounded generators.

Refined results for quantum dynamical semigroups with bounded generators.

Proved existence of quantum Zeno effect under weaker spectral gap assumptions.

Abstract

We prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For the case of a quantum dynamical semigroup with a bounded generator, our analysis leads to a refinement of existing results and extends them to a larger class of quantum operations. We also prove the existence of a novel strong quantum Zeno limit for quantum operations for which a certain spectral gap assumption, which all previous results relied on, is lifted. The quantum operations are instead required to satisfy a weaker property of strong power-convergence. In addition, we establish, for the first time, the existence of a quantum Zeno limit for the case of unbounded generators. We also provide a variety of physically interesting examples of quantum operations to which our results apply.