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The objective of this work is to develop a recursive, discrete time quantum filtering equation for a system that interacts with a probe, on which measurements are performed according to the Positive Operator Valued Measures (POVMs)…
We treat the events determined by a quantum physical state in a noncommutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued measures (POVMs). We consider in detail the…
Probability measures (quasi probability mass), given in the form of integrals of Wigner function over areas of the underlying phase space, give rise to operator valued probability measures (OVM). General construction methods of OVMs, are…
An implementation of the positive operator valued measure (POVM) is given. By using this POVM one can realize the probabilistic teleportation of an unknown two-particle state.
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…
In this paper we present a protocol for the implementation of a positive-operator-valued measure (POVM) on massive fermionic qubits. We present methods for implementing non-dispersive qubit transport, spin rotations and spin polarizing…
It is well known that, in the description of quantum observables, positive operator valued measures (POVMs) generalize projection valued measures (PVMs) and they also turn out be more optimal in many tasks. We show that a commutative POVM…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at…
Let $F$ be a Parseval frame in a Hilbert space and let $E$ be a set of real numbers. From these data, we construct an operator $H_{E,e}$ and a positive operator-valued measure (POVM) $F_{E,e}$. This paper investigates in detail the…
We provide a definition of POVM in terms of abstract tensor structure only. It is justified in two distinct manners. i. At this abstract level we are still able to prove Naimark's theorem, hence establishing a bijective correspondence…
We prove a theorem about positive-operator-valued measures (POVMs) that is an analog of the Kolmogorov extension theorem, a standard theorem of probability theory. According to our theorem, if a sequence of POVMs G_n on $\mathbb{R}^n$…
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…
We introduce positive operator-valued measure (POVM) generated by the projective unitary representation of a direct product of locally compact Abelian group $G$ with its dual $\hat G$. The method is based upon the Pontryagin duality…
In a recent paper, Buscemi and al. defined a notion of clean positive operator valued measures (POVMs). We here characterize which POVMs are clean in some class that we call quasi-qubit POVMs, namely POVMs whose elements are all rank-one or…
We construct relational observables in group field theory (GFT) in terms of covariant positive operator-valued measures (POVMs), using techniques developed in the context of quantum reference frames. We focus on matter quantum reference…
We obtain a formal characterization of the compatibility or otherwise of a set of positive-operator-valued measures (POVMs) via their Naimark extensions. We show that a set of POVMs is jointly measurable if and only if there exists a single…
Born's rule in its conventional textbook form applies to the small class of projective measurements only. It is well-known that a generalization of Born's rule to realistic experiments must be phrased in terms of positive operator valued…
It is commonly believed that the most general type of a quantum-mechanical measurement is one described by a positive-operator valued measure (POVM). In the present paper, this statement is proven for any measurements on quantum systems…
A suitable generalized measurement described by a 4-element positive operator-valued measure (POVM) on each particle of a two-qubit system in the singlet state is, from the point of view of Einstein, Podolsky, and Rosen's (EPR's) criterion…