Related papers: On constructing informationally complete covariant…
Let $(X,+,d)$ be an Abelian metric group and $A\subset X$. We investigate the spectre of a set $A$, defined as the set of all elements $z\in X$ such that for every $x\in A$ either $x+z \in A$ or $x-z \in A$. We consider the corresponding to…
We construct a family of operator systems and $k$-AOU spaces generated by a finite number of projections satisfying a set of linear relations. This family is universal in the sense that the map sending the generating projections to any…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
We analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme…
We show that the correct mathematical foundation of quantum decision theory, dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of the projection-valued measure. The latter is…
We study the quantum ($C^*$) convexity structure of normalized positive operator valued measures (POVMs) on measurable spaces. In particular, it is seen that unlike extreme points under classical convexity, $C^*$-extreme points of…
We consider a class of non-locally compact groups on which one may define a left-invariant, finitely additive measure taking values in some finitely generated extension of the field $\mathbb{R}$ of real numbers. In particular, we recover…
In order to find out for which initial states of the system the uncertainty of the measurement outcomes will be minimal, one can look for the minimizers of the Shannon entropy of the measurement. In case of group covariant measurements this…
We examine rigidity phenomena for representations of amenable operator algebras which have an ideal of compact operators. We establish that a generalized version of Kadison's conjecture on completely bounded homomorphisms holds for the…
The expectation values of a hermitean operator A in (2s+1)(2s+1) specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other (2s+1)(2s+1) coherent states also provide a basis for…
In this note, we consider a class of composition operators on Lebesgue spaces with variable exponents over metric measure spaces. Taking advantage of the compatibility between the metric-measurable structure and the regularity properties of…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider in this paper the reverse: for a positive matrix in the Hardy…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
By means of the technique of integration within an ordered product of operators and Dirac notation, we introduce a new kind of asymmetric integration projection operators in entangled state representations. These asymmetric projection…
We address the class of positive operator-valued measures (POVMs) for qubit systems that are obtained by coupling the signal qubit with a probe qubit and then performing a projective measurement on the sole probe system. These POVMs, which…
Inspired by some problems in Quantum Information Theory, we present some results concerning decompositions of positive operators acting on finite dimensional Hilbert spaces. We focus on decompositions by families having geometrical symmetry…
(This is a report for the Proceedings of ``Journees Relativistes 1993'' written in September 1993. Containes a short description of the results published elsewhere in the joint paper with A. Ashtekar) Integral calculus on the space of gauge…
The concept of intrinsic and operational observables in quantum mechanics is introduced. It is argued that, in any realistic description of a quantum measurement that includes a detecting device, it is possible to construct from the…
We study fixed points of contractive convolution operators associated to contractive quantum measures on locally compact quantum groups. We characterise the existence of non-zero fixed points respectively on $L^\infty(\mathbb{G})$ and on…