Related papers: Conditioned Observables in Quantum Mechanics
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,…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more…
Our basic concept is the set $\mathcal{E}(H)$ of effects on a finite dimensional complex Hilbert space $H$. If $a,b\in\mathcal{E}(H)$, we define the sequential product $a[\mathcal{I}]b$ of $a$ then $b$. The sequential product depends on the…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including…
We first show that every operation possesses an unique dual operation and measures an unique effect. If $a$ and $b$ are effects and $J$ is an operation that measures $a$, we define the sequential product of $a$ then $b$ relative to $J$.…
We present a characterization of the standard sequential product of quantum effects. The characterization is in term of algebraic, continuity and duality conditions that can be physically motivated.
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
This article points out that observables and instruments can be combined in many ways that have natural and physical interpretations. We shall mainly concentrate on the mathematical properties of these combinations. Section~1 reviews the…
We begin with a study of operations and the effects they measure. We define the probability that an effect $a$ occurs when the system is in a state $\rho$ by $P_\rho (a)= tr(\rho a)$. If $P_\rho (a)\ne 0$ and $\mathcal{I}$ is an operation…
Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…
In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In…
The concept of intrinsic and operational observables in quantum mechanics is introduced. In any realistic description of a quantum measurement that includes a macroscopic detecting device, it is possible to construct from the statistics of…
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…
We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
There is a multitude of interpretations of quantum mechanics, but foundational principles are lacking. Relational quantum mechanics views the observer as a physical system, which allows for an unambiguous interpretation as all axioms are…
In this paper, we present a collection of results on the observability of quantum mechanical systems, in the case the output is the result of a discrete nonselective measurement. By defining an effective observable we extend previous…
We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a…
Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may…