Quantum Incompatibility of a Physical Context

Abstract

Pivotal within quantum physics, the concept of quantum incompatibility is generally related to algebraic aspects of the formalism, such as commutation relations and unbiasedness of bases. Recently, the concept was identified as a resource in tasks involving quantum state discrimination and quantum programmability. Here we link quantum incompatibility with the amount of information that can be extracted from a system upon successive measurements of noncommuting observables, a scenario related to communication tasks. This approach leads us to characterize incompatibility as a resource encoded in a physical context, which involves both the quantum state and observables. Moreover, starting with a measure of context incompatibility we derive a measurement-incompatibility quantifier that is easily computable, admits a geometrical interpretation, and is maximum only if the eigenbases of the involved observables are mutually unbiased.

arXiv comment5+4 pages, 1 figure

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Cited by in corpus (9)

• Quantum resource covariance
• Classification of incompatibility for two orthonormal bases
• Uncertainty limits of the information exchange between a quantum system and an external meter
• Predictability as a quantum resource
• Geometric monotones of violations of quantum realism
• Certifying nonstabilizerness in quantum processors
• Measure of set imaginarity
• Information leak and incompatibility of physical context: A modified approach
• Theory-Independent Context Incompatibility: Quantification and Experimental Demonstration