225 research outputs found
Entropic uncertainty relations for electromagnetic beams
The symplectic tomograms of 2D Hermite--Gauss beams are found and expressed
in terms of the Hermite polynomials squared. It is shown that measurements of
optical-field intensities may be used to determine the tomograms of
electromagnetic-radiation modes. Furthermore, entropic uncertainty relations
associated with these tomograms are found and applied to establish the
compatibility conditions of the the field profile properties with
Hermite--Gauss beam description. Numerical evaluations for some Hermite--Gauss
modes illustrating the corresponding entropic uncertainty relations are finally
given.Comment: Invited talk at the XV Central European Workshop on Quantum Optics
(Belgrade, Serbia, 30 May -- 3 June 2008), to appear in Physica Scripta
On the connection between Complementarity and Uncertainty Principles in the Mach-Zehnder interferometric setting
We revisit, in the framework of Mach-Zehnder interferometry, the connection
between the complementarity and uncertainty principles of quantum mechanics.
Specifically, we show that, for a pair of suitably chosen observables, the
trade-off relation between the complementary path information and fringe
visibility is equivalent to the uncertainty relation given by Schr\"odinger
and Robertson, and to the one provided by Landau and Pollak as well. We also
employ entropic uncertainty relations (based on R\'enyi entropic measures) and
study their meaning for different values of the entropic parameter. We show
that these different values define regimes which yield qualitatively different
information concerning the system, in agreement with findings of [A. Luis,
Phys. Rev. A 84, 034101 (2011)]. We find that there exists a regime for which
the entropic uncertinty relations can be used as criteria to pinpoint non
trivial states of minimum uncertainty.Comment: 7 pages, 2 figure
New uncertainty relations for tomographic entropy: Application to squeezed states and solitons
Using the tomographic probability distribution (symplectic tomogram)
describing the quantum state (instead of the wave function or density matrix)
and properties of recently introduced tomographic entropy associated with the
probability distribution, the new uncertainty relation for the tomographic
entropy is obtained. Examples of the entropic uncertainty relation for squeezed
states and solitons of the Bose--Einstein condensate are considered.Comment: 18 pages, 2 figures, to be published in European Physical Journal
Alternative commutation relations, star products and tomography
Invertible maps from operators of quantum obvservables onto functions of
c-number arguments and their associative products are first assessed. Different
types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution
are discussed. The recently introduced symplectic tomography map of observables
(tomograms) related to the Heisenberg-Weyl group is shown to belong to the
standard framework of the maps from quantum observables onto the c-number
functions. The star-product for symbols of the quantum-observable for each one
of the maps (including the tomographic map) and explicit relations among
different star-products are obtained. Deformations of the Moyal star-product
and alternative commutation relations are also considered.Comment: LATEX plus two style files, to appear in J. Phys.
Nonclassical Light in Interferometric Measurements
It is shown that the even and odd coherent light and other nonclassical
states of light like superposition of coherent states with different phases may
replace the squeezed light in interferometric gravitational wave detector to
increase its sensitivity. (Contribution to the Second Workshop on Harmonic
Oscillator, Cocoyoc, Mexico, March 1994)Comment: 8 pages,LATEX,preprint of Naples University,
INFN-NA-IV-94/30,DSF-T-94/3
Distances between quantum states in the tomographic-probability representation
Distances between quantum states are reviewed within the framework of the
tomographic-probability representation. Tomographic approach is based on
observed probabilities and is straightforward for data processing. Different
states are distinguished by comparing corresponding probability-distribution
functions. Fidelity as well as other distance measures are expressed in terms
of tomograms.Comment: 10 pages, Contribution to the 16th Central European Workshop on
Quantum Optics (CEWQO'09), May 23-27, 2009, Turku, Finlan
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