Related papers: Post-processing minimal joint observables
Joint measurements of qubit observables have recently been studied in conjunction with quantum information processing tasks such as cloning. Considerations of such joint measurements have until now been restricted to a certain class of…
For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly…
Recently a problem concerning the equivalence of joint measurability and coexistence of quantum observables was solved [15]. In this paper we generalize two known joint measurability results from sharp observables to the class of extreme…
In order to analyze joint measurability of given measurements, we introduce a Hermitian operator-valued measure, called $W$-measure, such that it has marginals of positive operator-valued measures (POVMs). We prove that ${W}$-measure is a…
Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity…
We show that there are informationally complete joint measurements of two conjugated observables on a finite quantum system, meaning that they enable to identify all quantum states from their measurement outcome statistics. We further…
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…
Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the…
To effectively utilize quantum incompatibility as a resource in quantum information processing, it is crucial to evaluate how incompatible a set of devices is. In this study, we propose an ordering to compare incompatibility and reveal its…
Three notions of complementarity - operational, probabilistic, and value complementarity - are reanalysed with respect to the question of joint measurements and compared with reference to some examples of canonically conjugate observables.…
For a quantum measurement process described by a quantum instrument $\mathcal{I}$ and a system observable corresponding to a positive-operator valued measure (POVM) $E ,$ $\mathcal{I}$ is said to conserve the information of $E$ if the joint…
This paper presents some of the basic properties of conditioned observables in finite-dimensional quantum mechanics. We begin by defining the sequential product of quantum effects and use this to define the sequential product of two…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
One of the most intriguing aspects of Quantum Mechanics is the impossibility of measuring at the same time observables corresponding to non-commuting operators. This impossibility can be partially relaxed when considering joint or…
Measurements in quantum theory exhibit incompatibility, i.e., they can fail to be jointly measurable. An intuitive way to represent the (in)compatibility relations among a set of measurements is via a hypergraph representing their joint…
Weak measurements are a new tool for characterizing post-selected quantum systems during their evolution. Weak measurement was originally formulated in terms of von Neumann interactions which are practically available for only the simplest…
Unavoidable disturbance caused by a quantum measurement implies that the realizable subsequent measurements are getting limited after one performs some measurement. The obvious general limitation that one cannot circumvent by sequential or…
In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of…
The concept of a modular value of an observable of a pre- and post-selected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an…
We give an overview of joint unsharp measurements of non-commuting observables using positive operator valued measures (POVMs). We exemplify the role played by joint measurability of POVMs in entropic uncertainty relation for Alice's pair…