3,493 research outputs found
Number-phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra
In this letter, the number-phase entropic uncertainty relation and the
number-phase Wigner function of generalized coherent states associated to a few
solvable quantum systems with nondegenerate spectra are studied. We also
investigate time evolution of number-phase entropic uncertainty and Wigner
function of the considered physical systems with the help of temporally stable
Gazeau-Klauder coherent states.Comment: 10 pages, 9 figures; To appear in Phys Lett A 200
Entropic Uncertainty Relations in Quantum Physics
Uncertainty relations have become the trademark of quantum theory since they
were formulated by Bohr and Heisenberg. This review covers various
generalizations and extensions of the uncertainty relations in quantum theory
that involve the R\'enyi and the Shannon entropies. The advantages of these
entropic uncertainty relations are pointed out and their more direct connection
to the observed phenomena is emphasized. Several remaining open problems are
mentionedComment: 35 pages, review pape
Entropic uncertainty relations for extremal unravelings of super-operators
A way to pose the entropic uncertainty principle for trace-preserving
super-operators is presented. It is based on the notion of extremal unraveling
of a super-operator. For given input state, different effects of each
unraveling result in some probability distribution at the output. As it is
shown, all Tsallis' entropies of positive order as well as some of Renyi's
entropies of this distribution are minimized by the same unraveling of a
super-operator. Entropic relations between a state ensemble and the generated
density matrix are revisited in terms of both the adopted measures. Using
Riesz's theorem, we obtain two uncertainty relations for any pair of
generalized resolutions of the identity in terms of the Renyi and Tsallis
entropies. The inequality with Renyi's entropies is an improvement of the
previous one, whereas the inequality with Tsallis' entropies is a new relation
of a general form. The latter formulation is explicitly shown for a pair of
complementary observables in a -level system and for the angle and the
angular momentum. The derived general relations are immediately applied to
extremal unravelings of two super-operators.Comment: 8 pages, one figure. More explanations are given for Eq. (2.19) and
Example III.5. One reference is adde
Entanglement, Purity, and Information Entropies in Continuous Variable Systems
Quantum entanglement of pure states of a bipartite system is defined as the
amount of local or marginal ({\em i.e.}referring to the subsystems) entropy.
For mixed states this identification vanishes, since the global loss of
information about the state makes it impossible to distinguish between quantum
and classical correlations. Here we show how the joint knowledge of the global
and marginal degrees of information of a quantum state, quantified by the
purities or in general by information entropies, provides an accurate
characterization of its entanglement. In particular, for Gaussian states of
continuous variable systems, we classify the entanglement of two--mode states
according to their degree of total and partial mixedness, comparing the
different roles played by the purity and the generalized entropies in
quantifying the mixedness and bounding the entanglement. We prove the existence
of strict upper and lower bounds on the entanglement and the existence of
extremally (maximally and minimally) entangled states at fixed global and
marginal degrees of information. This results allow for a powerful, operative
method to measure mixed-state entanglement without the full tomographic
reconstruction of the state. Finally, we briefly discuss the ongoing extension
of our analysis to the quantification of multipartite entanglement in highly
symmetric Gaussian states of arbitrary -mode partitions.Comment: 16 pages, 5 low-res figures, OSID style. Presented at the
International Conference ``Entanglement, Information and Noise'', Krzyzowa,
Poland, June 14--20, 200
A survey of uncertainty principles and some signal processing applications
The goal of this paper is to review the main trends in the domain of
uncertainty principles and localization, emphasize their mutual connections and
investigate practical consequences. The discussion is strongly oriented
towards, and motivated by signal processing problems, from which significant
advances have been made recently. Relations with sparse approximation and
coding problems are emphasized
Multidimensional entropic uncertainty relation based on a commutator matrix in position and momentum spaces
The uncertainty relation for continuous variables due to Byalinicki-Birula
and Mycielski expresses the complementarity between two -uples of
canonically conjugate variables and in terms of Shannon differential entropy. Here, we consider the
generalization to variables that are not canonically conjugate and derive an
entropic uncertainty relation expressing the balance between any two
-variable Gaussian projective measurements. The bound on entropies is
expressed in terms of the determinant of a matrix of commutators between the
measured variables. This uncertainty relation also captures the complementarity
between any two incompatible linear canonical transforms, the bound being
written in terms of the corresponding symplectic matrices in phase space.
Finally, we extend this uncertainty relation to R\'enyi entropies and also
prove a covariance-based uncertainty relation which generalizes Robertson
relation.Comment: 8 pages, 1 figur
Continuous-variable entropic uncertainty relations
Uncertainty relations are central to quantum physics. While they were
originally formulated in terms of variances, they have later been successfully
expressed with entropies following the advent of Shannon information theory.
Here, we review recent results on entropic uncertainty relations involving
continuous variables, such as position and momentum . This includes the
generalization to arbitrary (not necessarily canonically-conjugate) variables
as well as entropic uncertainty relations that take - correlations into
account and admit all Gaussian pure states as minimum uncertainty states. We
emphasize that these continuous-variable uncertainty relations can be
conveniently reformulated in terms of entropy power, a central quantity in the
information-theoretic description of random signals, which makes a bridge with
variance-based uncertainty relations. In this review, we take the quantum
optics viewpoint and consider uncertainties on the amplitude and phase
quadratures of the electromagnetic field, which are isomorphic to and ,
but the formalism applies to all such variables (and linear combinations
thereof) regardless of their physical meaning. Then, in the second part of this
paper, we move on to new results and introduce a tighter entropic uncertainty
relation for two arbitrary vectors of intercommuting continuous variables that
take correlations into account. It is proven conditionally on reasonable
assumptions. Finally, we present some conjectures for new entropic uncertainty
relations involving more than two continuous variables.Comment: Review paper, 42 pages, 1 figure. We corrected some minor errors in
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