703 research outputs found
General radiation states and Bell's inequalities
The connection between quantum optical nonclassicality and the violation of
Bell's inequalities is explored. Bell type inequalities for the electromagnetic
field are formulated for general states(arbitrary number or photons, pure or
mixed) of quantised radiation and their violation is connected to other
nonclassical properties of the field. Classical states are shown to obey these
inequalities and for the family of centered Gaussian states the direct
connection between violation of Bell-type inequalities and squeezing is
established.Comment: 4-pages in revtex with one ps figure include
The Schwinger SU(3) Construction - II: Relations between Heisenberg-Weyl and SU(3) Coherent States
The Schwinger oscillator operator representation of SU(3), studied in a
previous paper from the representation theory point of view, is analysed to
discuss the intimate relationships between standard oscillator coherent state
systems and systems of SU(3) coherent states. Both SU(3) standard coherent
states, based on choice of highest weight vector as fiducial vector, and
certain other specific systems of generalised coherent states, are found to be
relevant. A complete analysis is presented, covering all the oscillator
coherent states without exception, and amounting to SU(3) harmonic analysis of
these states.Comment: Latex, 51 page
Parametrizing the mixing matrix : A unified approach
A unified approach to parametrization of the mixing matrix for
generations is developed. This approach not only has a clear geometrical
underpinning but also has the advantage of being economical and recursive and
leads in a natural way to the known phenomenologically useful parametrizations
of the mixing matrix.Comment: 8 pages, LaTe
Moments of the Wigner Distribution and a Generalized Uncertainty Principle
The nonnegativity of the density operator of a state is faithfully coded in
its Wigner distribution, and this places constraints on the moments of the
Wigner distribution. These constraints are presented in a canonically invariant
form which is both concise and explicit. Since the conventional uncertainty
principle is such a constraint on the first and second moments, our result
constitutes a generalization of the same to all orders. Possible application in
quantum state reconstruction using optical homodyne tomography is noted.Comment: REVTex, no figures, 9 page
Entanglement and Complete Positivity: Relevance and Manifestations in Classical Scalar Wave Optics
Entanglement of states and Complete Positivity of maps are concepts that have
achieved physical importance with the recent growth of quantum information
science. They are however mathematically relevant whenever tensor products of
complex linear (Hilbert) spaces are involved. We present such situations in
classical scalar paraxial wave optics where these concepts play a role:
propagation characteristics of coherent and partially coherent Gaussian beams;
and the definition and separability of the family of Twisted Gaussian Schell
Model (TGSM) beams. In the former, the evolution of the width of a projected
one-dimensional beam is shown to be a signature of entanglement in a
two-dimensional amplitude. In the latter, the partial transpose operation is
seen to explain key properties of TGSM beams.Comment: 7 pages Revtex 4-
A classical optical approach to the `non-local Pancharatnam-like phases' in Hanbury-Brown-Twiss correlations
We examine a recent proposal to show the presence of nonlocal Pancharatnam
type geometric phases in a quantum mechanical treatment of intensity
interferometry measurements upon inclusion of polarizing elements in the setup.
It is shown that a completely classical statistical treatment of such effects
is adequate for practical purposes. Further we show that the phase angles that
appear in the correlations, while at first sight appearing to resemble
Pancharatnam phases in their mathematical structure, cannot actually be
interpreted in that manner. We also describe a simpler Mach-Zehnder type setup
where similar effects can be observed without use of the paraxial
approximation.Comment: Minor corrections, published versio
The Hamilton--Jacobi Theory and the Analogy between Classical and Quantum Mechanics
We review here some conventional as well as less conventional aspects of the
time-independent and time-dependent Hamilton-Jacobi (HJ) theory and of its
connections with Quantum Mechanics. Less conventional aspects involve the HJ
theory on the tangent bundle of a configuration manifold, the quantum HJ
theory, HJ problems for general differential operators and the HJ problem for
Lie groups.Comment: 42 pages, LaTeX with AIMS clas
Landau Levels in the noncommutative
We formulate the Landau problem in the context of the noncommutative analog
of a surface of constant negative curvature, that is surface, and
obtain the spectrum and contrast the same with the Landau levels one finds in
the case of the commutative space.Comment: 19 pages, Latex, references and clarifications added including 2
figure
Wigner distributions for finite state systems without redundant phase point operators
We set up Wigner distributions for state quantum systems following a
Dirac inspired approach. In contrast to much of the work on this case,
requiring a phase space, particularly when is even, our
approach is uniformly based on an phase space grid and thereby
avoids the necessity of having to invoke a `quadrupled' phase space and hence
the attendant redundance. Both odd and even cases are analysed in detail
and it is found that there are striking differences between the two. While the
odd case permits full implementation of the marginals property, the even
case does so only in a restricted sense. This has the consequence that in the
even case one is led to several equally good definitions of the Wigner
distributions as opposed to the odd case where the choice turns out to be
unique.Comment: Latex, 14 page
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