115 research outputs found
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
Optical tomography of Fock state superpositions
We consider optical tomography of photon Fock state superpositions in
connection with recent experimental achievements. The emphasis is put on the
fact that it suffices to represent the measured tomogram as a main result of
the experiment. We suggest a test for checking the correctness of experimental
data. Explicit expressions for optical tomograms of Fock state superpositions
are given in terms of Hermite polynomials. Particular cases of vacuum and low
photon-number state superposition are considered as well as influence of
thermal noise on state purity is studied.Comment: 5 pages, 2 figure
Energy-Sensitive and "Classical-like" Distances Between Quantum States
We introduce the concept of the ``polarized'' distance, which distinguishes
the orthogonal states with different energies. We also give new inequalities
for the known Hilbert-Schmidt distance between neighbouring states and express
this distance in terms of the quasiprobability distributions and the normally
ordered moments. Besides, we discuss the distance problem in the framework of
the recently proposed ``classical-like'' formulation of quantum mechanics,
based on the symplectic tomography scheme. The examples of the Fock, coherent,
``Schroedinger cats,'' squeezed, phase, and thermal states are considered.Comment: 23 pages, LaTex, 2 eps figures, to appear in Physica Script
The Pauli Equation for Probability Distributions
The "marginal" distributions for measurable coordinate and spin projection is
introduced. Then, the analog of the Pauli equation for spin-1/2 particle is
obtained for such probability distributions instead of the usual wave
functions. That allows a classical-like approach to quantum mechanics. Some
illuminating examples are presented.Comment: 14 pages, ReVTe
Bell's inequalities in the tomographic representation
The tomographic approach to quantum mechanics is revisited as a direct tool
to investigate violation of Bell-like inequalities. Since quantum tomograms are
well defined probability distributions, the tomographic approach is emphasized
to be the most natural one to compare the predictions of classical and quantum
theory. Examples of inequalities for two qubits an two qutrits are considered
in the tomographic probability representation of spin states.Comment: 11 pages, comments and references adde
Mutually unbiased bases: tomography of spin states and star-product scheme
Mutually unbiased bases (MUBs) are considered within the framework of a
generic star-product scheme. We rederive that a full set of MUBs is adequate
for a spin tomography, i.e. knowledge of all probabilities to find a system in
each MUB-state is enough for a state reconstruction. Extending the ideas of the
tomographic-probability representation and the star-product scheme to
MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin
states and operators are introduced, ordinary and dual star-product kernels are
found. Since MUB-projectors are to obey specific rules of the star-product
scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new
relations on triple- and four-products of MUB-projectors. Example of qubits is
considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is
discussed.Comment: 11 pages, 1 table, partially presented at the 17th Central European
Workshop on Quantum Optics (CEWQO'2010), June 6-11, 2010, St. Andrews,
Scotland, U
Tomograms and other transforms. A unified view
A general framework is presented which unifies the treatment of wavelet-like,
quasidistribution, and tomographic transforms. Explicit formulas relating the
three types of transforms are obtained. The case of transforms associated to
the symplectic and affine groups is treated in some detail. Special emphasis is
given to the properties of the scale-time and scale-frequency tomograms.
Tomograms are interpreted as a tool to sample the signal space by a family of
curves or as the matrix element of a projector.Comment: 19 pages latex, submitted to J. Phys. A: Math and Ge
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