$$C^*$$-Extreme Points of Positive Operator Valued Measures and Unital Completely Positive Maps

The Structure of C∗-extreme Points in Spaces of Completely Positive Linear Maps on C∗-algebras

If A is a unital C∗-algebra and if H is a complex Hilbert space, then the set SH(A) of all unital completely positive linear maps from A to the algebra B(H) of continuous linear operators on H is an operator-valued, or generalised, state space of A. The usual state space of A occurs with the one-dimensional Hilbert space C. The structure of the extreme points of generalised state spaces was det...

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.

Unital Positive Maps and Quantum States

We analyze the structure of the subset of states generated by unital completely positive quantum maps, A witness that certifies that a state does not belong to the subset generated by a given map is constructed. We analyse the representations of positive maps and their relation to quantum Perron-Frobenius theory. PACS: 03.65.Bz, 03.67.-a, 03.65.Yz

Positive Operator - Valued Measurements