A Retrodictive Approach to Quantum State Smoothing

TL;DR

This paper introduces a new quantum state smoothing method based on retrodiction that always produces physical states without environmental assumptions, improving state purity estimates.

Contribution

It proposes a novel retrodictive quantum smoothing approach that guarantees physical states and does not rely on unverifiable environmental assumptions.

Findings

Smoothed states have higher average purity than prior-based states.

The method always yields physical quantum states.

Connections made with existing smoothing theories.

Abstract

Smoothing is a technique for estimating the state of an imperfectly monitored open system by combining both prior and posterior measurement information. In the quantum regime, current approaches to smoothing either give unphysical outcomes, due to the non-commutativity of the measurements at different times, or require assumptions about how the environment is measuring the system, which with current technology is unverifiable. We propose a novel definition of the smoothed quantum state based on quantum Bayesian retrodiction, which mirrors the classical retrodictive approach to smoothing. This approach always yields physical results and does not require any assumption on the environment. We show that this smoothed state has, on average, greater purity than the state reconstructed using just the prior information. Finally, we make a connection with the smoothing theory of Guevara and Wiseman in a well-studied regime, and describe from a purely quantum perspective how it conditions on the posterior information.