Operational measure of incompatibility of noncommuting observables

Abstract

Uncertainty relations are often considered to be a measure of incompatibility of noncommuting observables. However, such a consideration is not valid in general, motivating the need for an alternate measure that applies to any set of noncommuting observables. We present an operational approach to quantifying incompatibility without invoking uncertainty relations. Our measure aims to capture the incompatibility of noncommuting observables as manifest in the non-orthogonality of their eigenstates. We prove that this measure has all the desired properties: it is zero when the observables commute, strictly greater than zero when they do not, and is maximum when they are mutually unbiased. We also obtain tight upper bounds on this measure for any N noncommuting observables and compute it exactly when the observables are mutually unbiased.

7 pages; title modified and other minor changes, references added; journal version

References in corpus (6)

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• Higher entropic uncertainty relations for anti-commuting observables
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Cited by in corpus (4)

• Measuring incompatibility and clustering quantum observables with a quantum switch
• Fine-grained uncertainty relations for several quantum measurements
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• On optimal cloning and incompatibility