Exact Stochastic Differential Equations for Quantum Reverse Diffusion

TL;DR

This paper develops exact stochastic differential equations for quantum reverse diffusion, enabling real-time quantum state recovery and noise mitigation in monitored quantum systems, with broad implications for quantum information processing.

Contribution

It introduces analytical SDEs for quantum reverse diffusion, extending forward dynamics to include non-Markovian stochastic drift, facilitating real-time quantum state control.

Findings

Derived exact stochastic differential equations for quantum reverse diffusion.

Showed that reverse processes can be implemented in real-time without variational methods.

Established a framework for quantum state recovery and noise-resilient quantum operations.

Abstract

The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic differential equations for quantum reverse diffusion, along with corresponding stochastic master equations. These equations describe the exact and approximate stochastic reverse processes for continuously monitored Pauli channels, including time-dependent depolarizing noise. We show that the reverse processes generalize the forward dynamics by combining the noise effects of the forward processes with an additional non-Markovian stochastic drift that dynamically steers a quantum state back to its initial configuration. Consequently, the exact SDEs admit closed-form solutions that can be implemented in real-time without the need for variational techniques. Our findings establish an analytical framework for quantum state recovery, noise-resilient quantum gates, quantum generative modelling, quantum tomography via forward-reverse cycles, and potential paradigms for quantum error correction based on reverse diffusion.