Related papers: Necessary and sufficient condition for joint measu…
Measurement incompatibility is one of the cornerstones of quantum theory. This phenomenon appears in many forms, of which the concept of non-joint measurability has received considerable attention in the recent years. In order to…
How much unavoidable randomness is generated by a Positive Operator Valued Measure (POVM)? We address this question using two complementary approaches. First we study the variance of a real variable associated to the POVM outcomes. In this…
Sufficient and necessary conditions are presented for the existence of $(N,M)$-positive operator valued measures ($(N,M)$-POVMs) valid for arbitrary-dimensional quantum systems. A sufficient condition for the existence of $(N,M)$-POVMs is…
The purpose of this note is to clarify the logical relationship between joint measurability and contextuality for quantum observables in view of recent developments [1-4].
A general formalism for joint weak measurements of a pair of complementary observables is given. The standard process of optical three-wave mixing in a nonlinear crystal (such as in parametric down-conversion) is suitable for such tasks. To…
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…
The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space…
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.
The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert…
A theory of joint nonideal measurement of incompatible observables is used in order to assess the relative merits of quantum tomography and certain measurements of generalized observables, with respect to completeness of the obtained…
We derive a measurement operator corresponding to a quantum nondemolition (QND) measurement of an atomic ensemble. The quantum measurement operator takes the form of a positive operator valued measure (POVM) and is valid for arbitrary…
We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). For informationally complete sets, we propose construction methods from orthonormal Hermitian operator…
It is a crucial feature of quantum mechanics that not all measurements are compatible with each other. However, if measurements suffer from noise they may lose their incompatibility. Here, we consider the effect of white noise and determine…
Joint or simultaneous measurements of non-commuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for defining what an "optimal" joint measurement is, with…
Joint quantum measurements of non-commuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the…
In contrast to a projective quantum measurement in which the system is projected onto an eigenstate of the measured operator, in a weak measurement the system is only weakly perturbed while only partial information on the measured…
We study the local implementation of POVMs when we require only the faithful reproduction of the statistics of the measurement outcomes for all initial states. We first demonstrate that any POVM with separable elements can be implemented by…
We discuss the problem of implementing generalized measurements (POVMs) with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an…
Incompatible observables underlie pillars of quantum physics such as contextuality and entanglement. The Heisenberg uncertainty principle is a fundamental limitation on the measurement of the product of incompatible observables, a `joint'…
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…