Incompatibility of unbiased qubit observables and Pauli channels

摘要

A quantum observable and a channel are considered compatible if they formparts of the same measurement device, otherwise they are incompatible.Constrains on compatibility between observables and channels can be quantifiedvia relations highlighting the necessary trade-offs between noise anddisturbance within quantum measurements. In this paper we shall discuss thegeneral properties of these compatibility relations, and then fullycharacterize the compatibility conditions for an unbiased qubit observable anda Pauli channel. The implications of the characterization are demonstrated onsome concrete examples.