Dynamics of a quantum reference frame undergoing selective measurements and coherent interactions

TL;DR

This paper investigates how a quantum directional reference frame evolves under repeated measurements and interactions, revealing complex dynamics and proposing strategies to correct drift using specific unitary operations.

Contribution

It introduces a detailed analysis of the dynamics of quantum reference frames under measurements and interactions, and proposes a method to eliminate drift with tailored unitaries.

Findings

Retaining measurement records reveals dynamics hidden in averaged data.

Repeated unitary interactions lead to different reference frame evolution than measurements.

A specific sequence of unitaries can effectively eliminate rotational drift.

Abstract

We consider the dynamics of a quantum directional reference frame undergoing repeated interactions. We first describe how a precise sequence of measurement outcomes affects the reference frame, looking at both the case that the measurement record is averaged over and the case wherein it is retained. We find, in particular, that there is interesting dynamics in the latter situation which cannot be revealed by considering the averaged case. We then consider in detail how a sequence of rotationally invariant unitary interactions affects the reference frame, a situation which leads to quite different dynamics than the case of repeated measurements. We then consider strategies for correcting reference frame drift if we are given a set of particles with polarization opposite to the direction of drift. In particular, we find that by implementing a suitably chosen unitary interaction after every two measurements we can eliminate the rotational drift of the reference frame.