Juha-Pekka Pellonpää

Covariant Phase Observables in Quantum Mechanics

In this paper we characterize all the phase shift covariant normalized positive operator measures, i.e., phase observables, and we investigate some of their examples. We also characterize those phase observables which arise from the phase space observables as their polar coordinate angle margins.

Characterizations of the canonical phase observable

In this paper we investigate various properties of phase observables which could serve to determine the canonical phase observable among the family of all phase observables. We also show that any contractive weighted shift operator defines a unique phase observable, and we characterize phase observables that give the most accurate phase distribution in coherent states in the classical limit.

Are number and phase complementary observables

We study various ways of characterizing the quantum optical number and phase as complementary observables.

Complete characterization of extreme quantum observables in infinite dimensions

We give a complete characterization for pure quantum measurements, i.e., for POVMs which are extremals in the convex set of all POVMs. Such measurements are free from classical noise. The characterization is valid both in discrete and continuous cases, and also in the case of an infinite Hilbert space. We show that sharp measurements are clean, i.e. they cannot be irreversibly connected to another POVMs via quantum channels and thus they are free from any additional quantum noise. We exhibit an example which demonstrates that this result could also be approximately true for pure measurements.We give a complete characterization for extreme quantum observables, i.e. for normalized positive operator valued measures (POVMs) which are extremals in the convex set of all POVMs. The characterization is valid both in discrete and continuous cases, and also in the case of an infinite-dimensional Hilbert space. We show that sharp POVMs are pre-processing clean, i.e. they cannot be irreversibly connected to other POVMs via quantum channels.We give a complete characterization for pure quantum measurements, i.e., for POVMs which are extremals in the convex set of all POVMs. Such measurements are free from classical noise. The characterization is valid both in discrete and continuous cases, and also in the case of an infinite Hilbert space. We show that sharp measurements are clean, i.e. they cannot be irreversibly connected to another POVMs via quantum channels and thus they are free from any additional quantum noise. We exhibit an example which demonstrates that this result could also be approximately true for pure measurements.

One-to-One Mapping between Steering and Joint Measurability Problems.

Quantum steering refers to the possibility for Alice to remotely steer Bobs state by performing local measurements on her half of a bipartite system. Two necessary ingredients for steering are entanglement and incompatibility of Alices measurements. In particular, it is known that for the case of pure states of maximal Schmidt rank the problem of steerability for Bobs assemblage is equivalent to the problem of joint measurability for Alices observables. We show that such an equivalence holds in general; namely, the steerability of any assemblage can always be formulated as a joint measurability problem, and vice versa. We use this connection to introduce steering inequalities from joint measurability criteria and develop quantifiers for the incompatibility of measurements.

The norm-1-property of a quantum observable

A normalized positive operator measure

Covariant localizations in the torus and the phase observables

X\mapsto E(X)

Operator integrals and phase space observables

has the norm-1-property if

Positive sesquilinear form measures and generalized eigenvalue expansions

\no{E(X)}=1

Quantum measurements on finite dimensional systems: relabeling and mixing

whenever