Incompatibility of unbiased qubit observables and Pauli channels

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.

10 pages, 6 figures

References in corpus (3)

• An Invitation to Quantum Incompatibility
• Incompatibility of quantum channels
• Approximating incompatible von Neumann measurements simultaneously

Cited by in corpus (11)

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• Compatibility of covariant quantum channels with emphasis on Weyl symmetry
• On the compatibility of quantum instruments
• Amount of quantum coherence needed for measurement incompatibility
• Quantifying unsharpness of observables in an outcome-independent way
• Measurement sharpness and disturbance tradeoff
• Noise-disturbance relation and the Galois connection of quantum measurements
• The unavoidable information flow to environment in quantum measurements
• Testing incompatibility of quantum devices with few states
• Comparing quantum incompatibility of device sets from an operational perspective
• Information leak and incompatibility of physical context: A modified approach