Quantum Zeno Dynamics through stochastic protocols

TL;DR

This paper investigates how stochastic timing in quantum measurements influences Zeno confinement, providing analytical expressions and numerical validation for different protocols, advancing quantum control techniques.

Contribution

It introduces a framework for understanding stochastic effects in Quantum Zeno Dynamics and adapts confinement protocols to stochastic scenarios with analytical and numerical validation.

Findings

Analytical expressions for survival probability in stochastic Zeno regimes

Successful adaptation of dissipative and coherent protocols to stochastic timing

Trade-offs identified between probabilistic high-fidelity and deterministic confinement schemes

Abstract

Quantum Zeno Dynamics is the phenomenon that the observation or strong driving of a quantum system can freeze its dynamics to a subspace, effectively truncating the Hilbert space of the system. It represents the quantum version of the famous flying arrow Zeno paradox. Here, we study how temporal stochasticity in the system observation (or driving) affects the survival probability of the system in the subspace. In particular, we introduce a strong and a weak Zeno regime for which we quantify the confinement by providing an analytical expression for this survival probability. We investigate several dissipative and coherent protocols to confine the dynamics, and show that they can be successfully adapted to the stochastic version. In the weak Zeno regime the dynamics within the subspace effectively acts as an additional source of stochasticity in the confinement protocol. Our analytical predictions are numerically tested and verified on a paradigmatic spin chain. As practical implications different coherent and dissipative confinement protocols allow to choose a trade-off between a probabilistic scheme with high fidelity (compared to perfect subspace dynamics) and a deterministic one with a slightly lower fidelity, which is a step towards better control in future quantum technologies.