Arrow of Time for Continuous Quantum Measurement

TL;DR

This paper explores the concept of the arrow of time in continuous quantum measurements, demonstrating that while individual measurement sequences can be reversed, a statistical arrow of time still emerges due to probabilistic differences.

Contribution

It introduces a framework to quantify the statistical arrow of time in continuous quantum measurements and shows the universality of reversibility in non-projective measurement sequences.

Findings

Time-reversed evolution is physically possible with negated measurement records.

A statistical arrow of time can be quantified by log-likelihood differences.

Reversibility is universal for non-projective measurement sequences.

Abstract

We investigate the statistical arrow of time for a quantum system being monitored by a sequence of measurements. For a continuous qubit measurement example, we demonstrate that time-reversed evolution is always physically possible, provided that the measurement record is also negated. Despite this restoration of dynamical reversibility, a statistical arrow of time emerges, and may be quantified by the log-likelihood difference between forward and backward propagation hypotheses. We then show that such reversibility is a universal feature of non-projective measurements, with forward or backward Janus measurement sequences that are time-reversed inverses of each other.