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Standard projective measurements represent a subset of all possible measurements in quantum physics, defined by positive-operator-valued measures. We study what quantum measurements are projective simulable, that is, can be simulated by using projective measurements and classical randomness. We first prove that every measurement on a given quantum system can be realised by classical processing of projective measurements on the system plus an ancilla of the same dimension. Then, given a general measurement in dimension two or three, we show that deciding whether it is projective-simulable can be solved by means of semi-definite programming. We also establish conditions for the simulation of measurements using projective ones valid for any dimension. As an application of our formalism, we improve the range of visibilities for which two-qubit Werner states do not violate any Bell inequality for all measurements. From an implementation point of view, our work provides bounds on the amount of noise a measurement tolerates before losing any advantage over projective ones.
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting eigenvalue di
We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum object. We
Optimization of the mean efficiency for unambiguous (or error free)discrimination among $N$ given linearly independent nonorthogonal states should be realized in a way to keep the probabilistic quantum mechanical interpretation. This imposes a condit
Quantum resource theories provide a diverse and powerful framework for extensively studying the phenomena in quantum physics. Quantum coherence, a quantum resource, is the basic ingredient in many quantum information tasks. It is a subject of broad a
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, eff