Related papers: A Kolmogorov Extension Theorem for POVMs
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…
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 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…
We present an operationally motivated treatment of quantum reference frames in the setting that the frame is a covariant positive operator valued measure (POVM) on a finite homogeneous space, generalising the principal homogeneous spaces…
The embedding theorem arises in several problems from analysis and geometry. The purpose of this paper is to provide a deeper understanding of analysis and geometry with a particular focus on embedding theorems on spaces of homogeneous type…
In a Generalised Probabilistic Theory (GPT) equipped additionally with some extra geometric structure we define the morphophoric measurements as those for which the measurement map sending states to distributions of the measurement results…
We construct a resource theory of sharpness for finite-dimensional positive operator-valued measures (POVMs), where the sharpness-non-increasing operations are given by quantum preprocessing channels and convex mixtures with POVMs whose…
We derive a generalization of the Perron-Frobenius theorem to time-varying row-stochastic matrices as follows: using Kolmogorov's concept of absolute probability sequences, which are time-varying analogs of principal eigenvectors, we…
It is well-known that the law of total probability does not hold in general in quantum theory. However, the recent arguments on some of the fundamental assumptions in quantum theory based on the extended Wigner's Friend scenario show a need…
The incompatibility of quantum measurements is a fundamental feature of quantum mechanics with profound implications for uncertainty relations and quantum information processing. In this paper, we extend the notion of {\em $s$-order…
Kolmogorovs axiomatic framework is the best-known approach to describing probabilities and, due to its use of the Lebesgue integral, leads to remarkably strong continuity properties. However, it relies on the specification of a probability…
It is well-known that for any non-constant polynomial $P$ with integer coefficients the sequence $(P(n))_{ n\in \mathbb N}$ has the property that there are infinitely many prime numbers dividing at least one term of this sequence.…
Let $C({\mathbb R}^n)$ denote the set of real valued continuous functions defined on ${\mathbb R}^n$. We prove that for every $n\ge 2$ there are positive numbers $\lambda _1 , \ldots , \lambda _n$ and continuous functions $\phi_1 ,\ldots ,…
The tight frames can be regarded as a particular case of POVMs (positive operator-valued measures describing generalized measurements), namely the case when all the operators are rank-one. Each orthonormal basis is a tight frame, and every…
This paper provides a general method for defining a generalized quantum observable (or POVM) that supplies properly normalized conditional probabilities for the time of occurrence (i.e., of detection). This method treats the time of…
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…
Using the Hellmann-Feynman theorem, a general comparison theorem is established for an eigenvalue equation of the form $(T+V)|\psi> = E|\psi>$, where $T$ is a kinetic part which depends only on momentums and $V$ is a potential which depends…
Loss induced generalized measurements have been introduced years ago as a mean to implement generalized quantum measurements (POVM). Here the original idea is extended to a complete equivalence of lossy evolution and a certain widely used…
Generalized quantum measurements (POVMs or POMs) are important for optimally extracting information for quantum communication and computation. The standard realization via the Neumark extension requires extensive resources in the form of…