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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 condition on a certain matrix to be positive semidefinite. We reformulated this condition in such a way that the conditioned optimization problem for the mean efficiency was reduced to finding an unconditioned maximum of a function defined on a unit $N$-sphere for equiprobable states and on an $N$-ellipsoid if the states are given with different probabilities. We established that for equiprobable states a point on the sphere with equal values of Cartesian coordinates, which we call symmetric point, plays a special role. Sufficient conditions for a vector set are formulated for which the mean efficiency for equiprobable states takes its maximal value at the symmetric point. This set, in particular, includes previously studied symmetric states. A subset of symmetric states, for which the optimal measurement corresponds to a POVM requiring a one-dimensional ancilla space is constructed. We presented our constructions of a POVM suitable for the ancilla space dimension varying from 1 till $N$ and the Neumarks extension differing from the existing schemes by the property that it is straightforwardly applicable to the case when it is desirable to present the whole space system + ancilla as the tensor product of a two-dimensional ancilla space and the $N$-dimensional system space.
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
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 project
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
Evaluating the amount of information obtained from nonorthogonal quantum states is an important topic in the field of quantum information. The commonly used evaluation method is Holevo bound, which only provides an upper bound for quantum measurement