T. HEINOSAARI

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.

We show that there are informationally complete joint measurements of two conjugated observables on a finite quantum system, meaning that they enable the identification of all quantum states from their measurement outcome statistics. We further demonstrate that it is possible to implement a joint observable as a sequential measurement. If we...

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 every Weyl-Heisenberg covariant observable can be implemented as a sequential measurement of two conjugate...

It has been recently shown that an observable that identifies all pure states of a d-dimensional quantum system has minimally 4d-4 outcomes or slightly less (the exact number depending on d). However, no simple construction of this type of minimal observable is known. We investigate covariant observables that identify all pure states and have...

We prove that, regardless of the choice of the angles defining them, three fractional Fourier transforms do not solve the phase retrieval problem. That is, there do not exist three angles such that any square integrable signal could be determined up to a constant phase by knowing only the three intensities of the corresponding fractional...

The purpose of quantum tomography is to determine an unknown quantum state from measurement outcome statistics. There are two obvious ways to generalize this setting. First, our task need not be the determination of any possible input state but only some input states, for instance pure states. Second, we may have some prior information, or...

We study various optimality criteria for quantum observables. Observables are represented as covariant positive operator valued measures and we consider the case when the symmetry group is compact. Phase observables are examined as an example.

Given a unitary representation U of a compact group G and a transitive G-space Omega, we characterize the extremal elements of the convex set of all U-covariant positive operator valued measures.