We investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable.
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2005 (v1)PublicationUploaded on: March 31, 2023
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2009 (v1)Publication
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.
Uploaded on: March 27, 2023 -
2006 (v1)Publication
No description
Uploaded on: April 14, 2023 -
2007 (v1)Publication
The intrinsic unsharpness of a quantum observable is studied by introducing the notion of resolution width. This quantification of accuracy is shown to be closely connected with the possibility of making approximately repeatable measurements. As a case study, the intrinsic unsharpness and approximate repeatability of position and momentum...
Uploaded on: April 14, 2023 -
2011 (v1)Publication
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...
Uploaded on: April 14, 2023 -
2008 (v1)Publication
We discuss why projection valued measures are not sufficient in the description of position and momentum of a one dimensional particle. A satisfactory solution is offered using positive operator measures. We also argue why the relevant positive operator measures, but not all, may be called unsharp observables.
Uploaded on: March 27, 2023 -
2012 (v1)Publication
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...
Uploaded on: March 27, 2023 -
2004 (v1)Publication
We characterize all position and momentum observables on R and on R-3. We study some of their operational properties and discuss their covariant joint observables.
Uploaded on: March 31, 2023 -
2003 (v1)Publication
Given an irreducible representation of a group G , we show that all the covariant positive operator valued measures based on G / Z , where Z is a central subgroup, are described by trace class, trace one positive operators.
Uploaded on: March 31, 2023 -
2009 (v1)Publication
No description
Uploaded on: April 14, 2023 -
2004 (v1)Publication
Given a unitary representation U of an Abelian group G and a subgroup H , we characterize the positive operator valued measures based on the quotient group G / H and covariant with respect to U. Some physical examples are considered. Among them, phase and phase-difference observables are particularly important
Uploaded on: April 14, 2023 -
2006 (v1)Publication
We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the re producing kernel. Moreover, for p = 2 we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending...
Uploaded on: March 25, 2023 -
2014 (v1)Publication
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...
Uploaded on: March 27, 2023 -
2009 (v1)Publication
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.
Uploaded on: March 31, 2023