Positive-Operator Valued Measure (POVM) Quantization

Positive-Operator Valued Measure (POVM) Quantization

We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on a normalized positive operator-valued measure. The latter are built from families of density operators labeled by points of the measure space. We especially focus on various probabilistic aspects of these constructions. Simple or more elaborate examples illustrate the proce...

Positive Operator - Valued Measurements

On positive operator-valued continuous maps

In the paper the geometric properties of the positive cone and positive part of the unit ball of the space of operator-valued continuous space are discussed. In particular we show that ext-ray C+(K,L(H)) = {R+1{k0}x⊗ x : x ∈ S(H), k0 is an isolated point of K} ext B+(C(K,L(H))) = s-ext B+(C(K,L(H))) = {f ∈ C(K,L(H) : f(K) ⊂ ext B+(L(H))}. Moreover we describe exposed, strongly exposed and denti...

Observables Generalizing Positive Operator Valued Measures

We discuss a generalization of POVM which is used in quantum-like modeling of mental processing.

Operator-valued tensors on manifolds

‎In this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎To this end‎, ‎we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎First‎, ‎we put forward the concept of operator-valued tensors and extend semi-Riemannian...