Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Modern Optics

The phase representation of covariant phase observables

Juha-Pekka Pellonpää

Published Sep 1, 2003• 1 citation
Publisher

Abstract

Covariant phase observables are obtained by defining simple conditions for mappings from the set of phase wave functions (unit vectors of the Hardy space) to the set of phase probability densities.The existence of phase probability density for any phase wave function, the existence of interference effects, and the natural phase shift covariance are those simple conditions.The nonlocalizability of covariant phase observables is proved.

DOI
10.1080/0950034031000077524

Related papers

THE PHASE REPRESENTATION OF COVARIANT PHASE OBSERVABLES

Juha-Pekka Pellonpää

Abstract. Covariant phase observables are obtained by defining simple conditions for mappings from the set of phase wave functions (unit vectors of the Hardy space) to the set of phase probability densities. The existence of phase probability density for any phase wave function, the existence of interference effects, and the natural phase shift covariance are those simple conditions. The nonlocalizability of covariant phase observables is proved.

•Jan 1, 2001•0 citations

The phase representation of covariant phase observables

Juha-Pekka Pellonpää

Covariant phase observables are obtained by defining simple conditions for mappings from the set of phase wavefunctions (unit vectors of the Hardy space) to the set of phase probability densities. The existence of phase probability density for any phase wavefunction, the existence of interference effects and the natural phase shift covariance are those simple conditions. The non-localizability of covariant phase observables is proved.

arXiv:quant-ph/0109026•Journal of Modern Optics•Sep 1, 2003•0 citations

On the structure of covariant phase observables

Juha-Pekka Pellonpää

We study the mathematical structure of covariant phase observables. Such observables can alternatively be expressed as phase matrices, as sequences of unit vectors, as sequences of phase states, or as equivalence classes of covariant trace-preserving operations. Covariant generalized operator measures are defined by structure matrices which form a W*-algebra with phase matrices as its subset. The properties of the Radon–Nikodým derivatives of phase probability measures are studied.

arXiv:quant-ph/0108105•Journal of Mathematical Physics•Mar 1, 2002•11 citations

ON THE STRUCTURE OF COVARIANT PHASE OBSERVABLES

Juha-Pekka Pellonpää

Abstract. We study the mathematical structure of covariant phase observables. Such an observable can alternatively be expressed as a phase matrix, as a sequence of unit vectors, as a sequence of phase states, or as an equivalent class of covariant trace-preserving operations. Covariant generalized operator measures are defined by structure matrices which form a W ∗-algebra with phase matrices as its subset. The properties of the Radon-Nikod´ym derivatives of phase probability measures are studied. 1.

•Jan 1, 2001•11 citations

Covariant localizations in the torus and the phase observables

Gianni Cassinelli, Ernesto De Vito, PEKKA J. LAHTI +1 more

We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is furnished and the commutative localizations are singled out. As a consequence, we also get a vector sequence characterization of the covariant phase observables.

arXiv:quant-ph/0105079•Journal of Mathematical Physics•Feb 1, 2002•26 citations

Phase-space representations of general statistical physical theories

Matthias Singer, Werner Stulpe

It is shown that Hilbert-space quantum mechanics and many other statistical theories can be represented on some phase space, in the sense that states can be identified with probability measures and observables can be described by functions. In the general context of statistical dualities, informationally complete observables are introduced and a theorem on their existence is proven. The correspondence between these observables and the injective affine mappings from the states into the probability measures on phase space, i.e., the phase-space representations, is pointed out. In particular, a description of all observables by functions is presented, such that all expectation values can, in arbitrarily good physical approximation, be calculated as integrals. Moreover, some new aspects of the particular case of those phase-space representations of quantum mechanics that are related to certain joint position-momentum observables are discussed.

Journal of Mathematical Physics•Jan 1, 1992•52 citations
Covariant phase observables are obtained by defining simple conditions for mappings from the set of phase wave functions (unit vectors of the Hardy space) to the set of phase probability densities.The existence of phase probability density for any phase wave function, the existence of interference effects, and the natural phase shift covariance are those simple conditions.The nonlocalizability of covariant phase observables is proved.
Abstract. We study the mathematical structure of covariant phase observables. Such an observable can alternatively be expressed as a phase matrix, as a sequence of unit vectors, as a sequence of phase states, or as an equivalent class of covariant trace-preserving operations. Covariant generalized operator measures are defined by structure matrices which form a W ∗-algebra with phase matrices as its subset. The properties of the Radon-Nikod´ym derivatives of phase probability measures are studied. 1.
It is shown that Hilbert-space quantum mechanics and many other statistical theories can be represented on some phase space, in the sense that states can be identified with probability measures and observables can be described by functions. In the general context of statistical dualities, informationally complete observables are introduced and a theorem on their existence is proven. The correspondence between these observables and the injective affine mappings from the states into the probability measures on phase space, i.e., the phase-space representations, is pointed out. In particular, a description of all observables by functions is presented, such that all expectation values can, in arbitrarily good physical approximation, be calculated as integrals. Moreover, some new aspects of the particular case of those phase-space representations of quantum mechanics that are related to certain joint position-momentum observables are discussed.