2,141 research outputs found
Sequential measurements of conjugate observables
No full textWe 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 observables. This method is applicable both in finite- and infinite-dimensional Hilbert spaces, therefore covering sequential spin component measurements as well as position-momentum sequential measurements
Informationally complete joint measurements on finite quantum systems
No full textWe 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 require minimal noise in the joint measurement, then the joint observable is unique. If d is odd, then this observable is informationally complete. But if d is even, then the joint observable is not informationally complete, and one has to allow more noise in order to obtain informational completeness
Position and momentum observables on R and on R^3
No full textWe characterize all position and momentum observables on R and on R^3, i.e. all observables satisfying a suitable covariance property under the action of the Galilei group. We show that each position (respectively, momentum) observable is a fuzzy version of sharp position (resp., momentum). We study some operational properties of position and momentum observables and discuss their covariant joint observables
On the coexistence of position and momentum observables
No full textWe investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable
Why unsharp observables?
No full textWe 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
Minimal covariant observables identifying all pure states
No full textIt has been recently shown by Heinosaari, Mazzarella and Wolf (2013) [1] 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 minimal number of outcomes. It is shown that the existence of this kind of observables depends on the dimension of the Hilbert space
Intrinsic unsharpness and approximate repeatability of quantum measurements
No full textThe 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 measurements are examined in detail
Super Distributions, Analytic and Algebraic Super Harish-Chandra pairs
No full textWe extend the theory of super Harish-Chandra pairs, originally developed by Kostant
and Koszul for smooth Lie supergroups, to algebraic supergroups over a field of
characteristic zero. We also review the corresponding complex analytic theory
and we give a characterization of the action of an algebraic (resp. complex
analytic) super Harish-Chandra pair on a supervariety (resp. complex analytic
supermanifold)
Covariant quantum instruments
No full textThe 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
Representations of Super Lie Groups: Some Remarks
No full textWe give a quick review of the basic aspects of the theory of representations of super Lie groups on finite-dimensional vector spaces. In particular, the various possible approaches to representations of super Lie groups, super Harish-Chandra pairs and actions are analyzed. A sketch of a general setting for induced representation is also presented and some basic examples of induced representations (i.e., special and odd induction) are given
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