Incompatibility of unbiased qubit observables and Pauli channels

TL;DR

This paper explores the compatibility constraints between unbiased qubit observables and Pauli channels, providing a full characterization and demonstrating implications through concrete examples.

Contribution

It offers a complete characterization of compatibility conditions between unbiased qubit observables and Pauli channels, advancing understanding of measurement trade-offs.

Findings

Compatibility conditions fully characterized

Concrete examples demonstrate implications

Trade-offs between noise and disturbance analyzed

Abstract

A quantum observable and a channel are considered compatible if they form parts of the same measurement device, otherwise they are incompatible. Constrains on compatibility between observables and channels can be quantified via relations highlighting the necessary trade-offs between noise and disturbance within quantum measurements. In this paper we shall discuss the general properties of these compatibility relations, and then fully characterize the compatibility conditions for an unbiased qubit observable and a Pauli channel. The implications of the characterization are demonstrated on some concrete examples.