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We revisit the problem of finding the Naimark extension of a probability operator-valued measure (POVM), i.e. its implementation as a projective measurement in a larger Hilbert space. In particular, we suggest an iterative method to build the projective measurement from the sole requirements of orthogonality and positivity. Our method improves existing ones, as it may be employed also to extend POVMs containing elements with rank larger than one. It is also more effective in terms of computational steps.
We introduce and study the entanglement breaking rank of an entanglement breaking channel. We show that the entanglement breaking rank of the channel $mathfrak Z: M_d to M_d$ defined by begin{align*} mathfrak Z(X) = frac{1}{d+1}(X+text{Tr}(X)mathbb I
We address the implementation of the positive operator-valued measure (POVM) describing the optimal M-outcomes discrimination of the polarization state of a single photon. Initially, the POVM elements are extended to projective operators by Naimark t
A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix playing t
From a geometric point of view, Paulis exclusion principle defines a hypersimplex. This convex polytope describes the compatibility of $1$-fermion and $N$-fermion density matrices, therefore it coincides with the convex hull of the pure $N$-represent
In this paper we examine a generalization of the symmetric informationally complete POVMs. SIC-POVMs are the optimal measurements for full quantum tomography, but if some parameters of the density matrix are known, then the optimal SIC POVM should be