Fisher information from stochastic quantum measurements

TL;DR

This paper explores how stochastic quantum measurements influence the survival probability of a quantum system, introducing a Fisher information measure that links measurement randomness to quantum Zeno effects and quantum metrology applications.

Contribution

It introduces a new Fisher information measure based on measurement stochasticity, providing a novel characterization of Zeno phenomena and implications for quantum sensing.

Findings

Fisher information depends on measurement stochasticity variation.

Zeno phenomena linked to sensitivity of survival probability.

Numerical example supports theoretical insights.

Abstract

The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the survival probability to find the system in a given Hilbert subspace at the end of the dynamical evolution. In particular, we analytically study the distinguishability of two different stochastic measurement sequences in terms of a new Fisher information measure depending on the variation of a function, instead of a finite set of parameters. We find a novel characterization of Zeno phenomena as the physical result of the random observation of the quantum system, linked to the sensitivity of the survival probability with respect to an arbitrary small perturbation of the measurement stochasticity. Finally, the implications on the Cram\'er-Rao bound are discussed, together with a numerical example. These results are expected to provide promising applications in quantum metrology towards future, more robust, noise-based quantum sensing devices.