Quantum Zeno effect: Quantum shuffling and Markovianity

TL;DR

This paper explores how repeated measurements in quantum systems lead to the quantum Zeno and anti-Zeno effects, linking these phenomena to Markovian dynamics and providing insights for quantum control.

Contribution

It introduces the concept of quantum shuffling as an analogy for measurement effects and connects the transition from anti-Zeno to Zeno behavior with Markovianity, offering a new framework for understanding quantum dynamics.

Findings

Quantum Zeno and anti-Zeno effects emerge as two limits of quantum shuffling.

Transition from anti-Zeno to Zeno behavior relates to the onset of Markovian dynamics.

Rapid quantum shuffling can suppress evolution, causing long-term system stability.

Abstract

The behavior displayed by a quantum system when it is perturbed by a series of von Neumann measurements along time is analyzed. Because of the similarity between this general process with giving a deck of playing cards a shuffle, here it is referred to as quantum shuffling, showing that the quantum Zeno and anti-Zeno effects emerge naturally as two time limits. Within this framework, a connection between the gradual transition from anti-Zeno to Zeno behavior and the appearance of an underlying Markovian dynamics is found. Accordingly, although a priori it might result counterintuitive, the quantum Zeno effect corresponds to a dynamical regime where any trace of knowledge on how the unperturbed system should evolve initially is wiped out (very rapid shuffling). This would explain why the system apparently does not evolve or decay for a relatively long time, although it eventually undergoes an exponential decay. By means of a simple working model, conditions characterizing the shuffling dynamics have been determined, which can be of help to understand and to devise quantum control mechanisms in a number of processes from the atomic, molecular and optical physics.