Related papers: A universal property for sequential measurement
We present a unified treatment of sequential measurements of two conjugate observables. Our approach is to derive a mathematical structure theorem for all the relevant covariant instruments. As a consequence of this result, we show that…
A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The C*-algebra generated by the partial isometries is thus a quotient of…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
We evaluate some finite and infinite sums involving $q$-trigonometric and $q$-digamma functions. Upon letting $q$ approach $1$, one obtains corresponding sums for the classical trigonometric and the digamma functions. Our key argument is a…
We deduce some growth properties of composite entire functions in the light of their relative $(p,q)$\ th order by extending some results of J. Tu, Z. X. Chen and X. M. Zheng.
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
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…
We obtain a far-reaching generalization (in several directions) of the theorem of A. Lambert on the existence of the projective tensor product of operator sequence spaces. This result is obtained in the context of spaces, generalizing…
We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility…
Every measurement determines a single value as its outcome, and yet quantum mechanics predicts it only probabilistically. The Kochen-Specker theorem and Bell's inequality are often considered to reject a realist view but favor a skeptical…
Orders and types of entire and meromorphic functions have been actively investigated by many authors. In the present paper, we aim at investigating some basic properties in connection with sum and product of relative $(p,q)$-$\varphi$…
We establish several deep existence criteria for conditional expectations on von Neumann algebras, and then apply this theory to develop a noncommutative theory of representing measures of characters of a function algebra. Our main cycle of…
Three recent arguments seek to show that the universal applicability of unitary quantum theory is inconsistent with the assumption that a well-conducted measurement always has a definite physical outcome. In this paper I restate and analyze…
A general method of investigation of the uniqueness property for $C^*$-algebra equipped with a circle gauge action is discussed. It unifies isomorphism theorems for various crossed products and Cuntz-Krieger uniqueness theorem for…
Two basic properties of the set of all probability measures on the set of quantum states and their corollaries are considered. Several applications of these properties to analysis of functional constructions widely used in quantum…
We give new proofs of two basic results in number theory: The law of quadratic reciprocity and the sign of the Gauss sum. We show that these results are encoded in the relation between the discrete Fourier transform and the action of the…
Any power series with unit constant term can be factored into an infinite product of the form $\prod_{n\geq 1} (1-q^n)^{-a_n}$. We give direct formulas for the exponents $a_n$ in terms of the coefficients of the power series, and vice…
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalises the ones given up to date.
This paper presents a simple generalization of causal consistency suited to any object defined by a sequential specification. As causality is captured by a partial order on the set of operations issued by the processes on shared objects…
The summatory function of a $q$-regular sequence in the sense of Allouche and Shallit is analysed asymptotically. The result is a sum of periodic fluctuations for eigenvalues of absolute value larger than the joint spectral radius of the…