Good Simulation of All Quantum Measurements by Projective Measurements

Explore a comprehensive lecture on the simulation of quantum measurements by projective measurements in finite-dimensional quantum systems. Delve into the work of Prof. Michał Oszmaniec from the Center for Theoretical Physics PAS and NASK, who demonstrates that applying depolarizing noise with constant visibility parameter enables the simulation of any Positive Operator-Valued Measure (POVM) through randomized implementation of projective measurements. Discover how this finding limits the asymptotic advantage of POVMs over projective measurements in various information-processing tasks, including state discrimination, shadow tomography, and quantum metrology. Learn about the applications of these results to quantum foundations, including improvements in the range of parameters for which Werner and isotropic states have local models for generalized measurements, and asymptotically tight bounds on critical visibility for jointly measurable POVMs. Gain insights into the technical aspects of the research, including recent advances in POVM simulation, the solution to the Kadison-Singer problem, and the dimension-deficient Naimark extension theorem.