Complete Resource Theory of Quantum Incompatibility as Quantum Programmability

Francesco Buscemi, Eric Chitambar, Wenbin Zhou

Research output: Contribution to journalArticlepeer-review


Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely nonclassical phenomenon provides a necessary ingredient in many quantum information tasks such as violating a Bell inequality or nonlocally steering part of an entangled state. In this Letter, we characterize incompatibility in terms of programmable measurement devices and the general notion of quantum programmability. This refers to the temporal freedom a user has in issuing programs to a quantum device. For devices with a classical control and classical output, measurement incompatibility emerges as the essential quantum resource embodied in their functioning. Based on the processing of programmable measurement devices, we construct a quantum resource theory of incompatibility. A complete set of convertibility conditions for programmable devices is derived based on quantum state discrimination with postmeasurement information.

Original languageEnglish (US)
Article number120401
JournalPhysical review letters
Issue number12
StatePublished - Mar 27 2020

ASJC Scopus subject areas

  • General Physics and Astronomy


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