Amount of quantum coherence needed for measurement incompatibility

Abstract

A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to the diagonal elements of any observable jointly measurable with it, leading to a general criterion for the coherence needed for incompatibility. Specialising to the case where the second observable is incoherent (diagonal), we develop a concrete method for solving incompatibility problems, tractable even in large systems by analytical bounds, without resorting to numerical optimisation. We verify the consistency of our method by a quick proof of the known noise bound for mutually unbiased bases, and apply it to study emergent classicality in the spin-boson model of an N-qubit open quantum system. Finally, we formulate our theory in an operational resource-theoretic setting involving "genuinely incoherent operations" used previously in the literature, and show that if the coherence is insufficient to sustain incompatibility, the associated joint measurements have sequential implementations via incoherent instruments.

19 pages, 3 figures, identical to published version

References in corpus (8)

• All sets of incompatible measurements give an advantage in quantum state discrimination
• Operational relevance of resource theories of quantum measurements
• Inverting quantum decoherence by classical feedback from the environment
• Set coherence: basis-independent quantification of quantum coherence
• Quantum Decoherence of Two Qubits
• Radon-Nikodym derivatives of quantum operations
• Interpreting quantum coherence through a quantum measurement process
• Constructing extremal compatible quantum observables by means of two mutually unbiased bases

Cited by in corpus (7)

• Distance-based resource quantification for sets of quantum measurements
• Naimark dilations of qubit POVMs and joint measurements
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Completeness Stability of Quantum Measurements
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
• Compressing continuous variable quantum measurements
• On compatibility of binary qubit measurements