Incompatibility of quantum measurements lies at the core of nearly all quantum phenomena, from Heisenberg’s Uncertainty Principle, to the violation of Bell inequalities, and all the way up to quantum computational speed-ups. Historically, quantum incompatibility has been considered only in a qualitative sense. However, recently various resource-theoretic approaches have been proposed that aim to capture incompatibility in an operational and quantitative manner. Previous results in this direction have focused on particular subsets of quantum measurements, leaving large parts of the total picture uncharted.
A work, which I wrote together with Eric Chitambar and Wenbin Zhou and was published yesterday on Physical Review Letters, proposes the first complete solution to this problem by formulating a resource theory of measurement incompatibility that allows free convertibility among all compatible measurements. As a result, we are now able to explain quantum incompatibility in terms of quantum programmability; namely, the ability to switch on the fly between incompatible measurements is seen as a resource. From this perspective, quantum measurement incompatibility is intrinsically a dynamical phenomenon that reveals itself in time as we try to control the system.