The Gisin-Percival Stochastic Schr\"{o}dinger Equation from Standard Quantum Filtering Theory

TL;DR

This paper demonstrates that the Gisin-Percival stochastic Schrödinger equation can be derived from standard quantum filtering theory and can be simulated using a feedback-controlled continuous measurement model.

Contribution

It establishes an equivalence between the Gisin-Percival quantum state diffusion and quantum trajectory models, linking stochastic equations to measurement-based quantum control.

Findings

Equivalence between Gisin-Percival equation and quantum trajectory models

Development of a feedback scheme to simulate quantum state diffusion

Insight into measurement-based quantum state evolution

Abstract

We show that the quantum state diffusion equation of Gisin and Percival, driven by complex Wiener noise, is equivalent up to a global stochastic phase to quantum trajectory models. With an appropriate feedback scheme, we set up an analogue continuous measurement model with exactly simulates the Gisin-Percival quantum state diffusion.