Implementation of group-covariant positive operator valued measures by orthogonal measurements

Implementation of Group-Covariant POVMs by Orthogonal Measurements

We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark’s theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to find an implementation of a given group-covariant POVM by a quantum circuit using its symmetry. Based on representation theory of the symmetry group we deve...

Extremal Covariant Positive Operator Valued Measures: the Case of a Compact Symmetry Group

In the modern theory of quantum mechanics, observables are represented as normalized positive operator valued measures (POVMs). The set of all POVMs having the same outcome space has natural convex structure. A convex mixture of two POVMs corresponds to a random choice between two measurement apparatuses. An extremal POVM thus describes an observable which is unaffected by this kind of randomne...

Positive Operator Valued Measures Covariant with Respect to an Abelian Group

Given a unitary representation U of an Abelian group G and a subgroup H, we characterise the positive operator valued measures based on the quotient group G/H and covariant with respect to U .

Positive Operator - Valued Measurements

Observables Generalizing Positive Operator Valued Measures

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