Quantifying the incompatibility of quantum measurements relative to a basis

Abstract

Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability distributions associated with different quantum measurements can be converted into one another by probabilistic post-processing. The induced preorder over quantum measurements is directly related to multivariate majorization and gives rise to families of monotones, i.e., scalar quantifiers that preserve the ordering. For the case of orthogonal measurement we establish a quantitative connection between incompatibility, quantum coherence and entropic uncertainty relations. We generalize the construction to arbitrary POVM measurements and report complete families of monotones.

arXiv commentConstruction generalized to include POVMs. A modified preorder, related to post-processing by stochastic matrices, is also included. New result on coherence. Improved exposition

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Cited by in corpus (8)

• Incompatible measurements in quantum information science
• Quantum coherence as a signature of chaos
• Random Matrix Theory of the Isospectral twirling
• Quantum coherence and the localization transition
• Amount of quantum coherence needed for measurement incompatibility
• Incompatibility of local measurements provide advantage in local quantum state discrimination
• A Note on Hierarchy of Quantum Measurement Incompatibilities
• Non-commutative Index of Measurement-only Entanglement Phase Transition