Detector dependency of diffusive quantum monitorings

TL;DR

This paper investigates the conditions under which the detector dependency of diffusive quantum monitoring can be demonstrated experimentally, providing a framework to rule out detector-independent models in open quantum systems.

Contribution

It introduces a semi-definite programming approach to determine necessary conditions and analyzes physical scenarios to identify feasible experimental setups for detector dependency demonstration.

Findings

Semi-definite programming efficiently determines necessary conditions.

Analysis of environmental couplings and monitorings identifies feasible experimental thresholds.

Comparison with previous literature suggests optimal detection strategies.

Abstract

Continuous measurements play a pivotal role in the study of dynamical open quantum systems. `Dyne' detections are among the most widespread and efficient measurement schemes, and give rise to quantum diffusion of the conditioned state. In this work we study under what conditions the detector dependency of the conditional state of a quantum system subject to diffusive monitoring can be demonstrated experimentally, in the sense of ruling our any detector-independent pure-state dynamical model for the system. We consider an arbitrary number L of environments to which the system is coupled, and an arbitrary number K of different types of dyne detections. We prove that non-trivial necessary conditions for such a demonstration can be determined efficiently by semi-definite programming. To determine sufficient conditions, different physical environmental couplings and Hamiltonians for a qubit, and different sets of diffusive monitorings are scrutinized. We compare the threshold efficiencies that are sufficient in the various cases, as well as cases previously considered in the literature, to suggest the most feasible experimental options.