A quantum reference frame size-accuracy trade-off for quantum channels

TL;DR

This paper investigates the relationship between the size of quantum reference frames and the accuracy of approximating quantum channels, demonstrating that larger frames are needed for non-covariant channels, with specific results for SU(2) symmetry.

Contribution

It extends the study of quantum reference frames from observables to quantum transformations, providing quantitative trade-offs for channel approximation.

Findings

Large reference frames are necessary for accurate approximation of non-covariant channels.

Quantitative bounds are established for the size-accuracy trade-off.

Results are specifically applied to SU(2) symmetric channels.

Abstract

The imposition of symmetry upon the nature and structure of quantum observables has recently been extensively studied, with quantum reference frames playing a crucial role. In this paper, we extend this work to quantum transformations, giving quantitative results showing, in direct analogy to the case of observables, that a "large" reference frame is required for non-covariant channels to be well approximated by covariant ones. We apply our findings to the concrete setting of SU(2) symmetry.