Related papers: On the Observables Describing a Quantum Reference …
This article considers quantum systems described by a finite-dimensional complex Hilbert space $H$. We first define the concept of a finite observable on $H$. We then discuss ways of combining observables in terms of convex combinations,…
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…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
We discuss the distinction between the notion of partial observable and the notion of complete observable. Mixing up the two is frequently a source of confusion. The distinction bears on several issues related to observability, such as (i)…
In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's…
We identify and study a particular class of distinguishability problems for quantum observables (POVMs), in which observables with permuted effects are involved, which we call as the labeling problem. Consequently, we identify the binary…
The standard formalism of quantum mechanics is extended to describe a total system including the reference system (RS), with respect to which the total system is described. The RS is assumed to be able to act as a measuring apparatus, with…
Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. It is postulated that a quantum…
In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical…
It is important problem to clarify the class of implementable quantum measurements from both fundamental and applicable viewpoints. Positive-Operator-Valued Measure (POVM) measurements are implementable by the indirect measurement methods,…
We discuss the necessity and the emergence of quantum reference frames when attempting to define a rest frame for mixed particles. We analyze the corresponding concept of frame dependent entanglement and how it could affect measurements on…
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
We explain the powerful role that operator-valued measures can play in quantizing any set equipped with a measure, for instance a group (resp. group coset) with its invariant (resp. quasi-invariant) measure. Coherent state quantization is a…
We describe how to define observables analogous to quantum fields for the semicontinuous limit recently introduced by Jones in the study of unitary representations of Thompson's groups $F$ and $T$. We find that, in terms of correlation…
There is ambitious pretension formulated by Weinberg \cite{W} that {\it any relativistic quantum theory will look at sufficiently low energy like a quantum field theory.} It is based on the observation that for formulation of quantum field…
In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…
Let us consider a Lie (super)algebra $G$ spanned by $T_{\alpha}$ where $T_{\alpha}$ are quantum observables in BV-formalism. It is proved that for every tensor $c^{\alpha_1...\alpha_k}$ that determines a homology class of the Lie algebra…
Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric…
The interpretation of quantum theory known as QBism argues that many elements of the formalism have a subjective interpretation. At the same time, QBism claims to be a broadly realist program. This implies that reality in QBism must be…