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 $N$ 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

Geometric phase for mixed states: a differential geometric approach

A new definition and interpretation of geometric phase for mixed state cyclic unitary evolution in quantum mechanics are presented. The pure state case is formulated in a framework involving three selected Principal Fibre Bundles, and the well known Kostant-Kirillov-Souriau symplectic structure on (co) adjoint orbits associated with Lie groups. It is shown that this framework generalises in a natural and simple manner to the mixed state case. For simplicity, only the case of rank two mixed state density matrices is considered in detail. The extensions of the ideas of Null Phase Curves and Pancharatnam lifts from pure to mixed states are also presented.Comment: 22 pages, revtex

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

Transmission and reflection of Gaussian beams by anisotropic parallel plates

Explicit and compact expressions describing the reflection and the transmission of a Gaussian beam by anisotropic parallel plates are given. Multiple reflections inside the plate are taken into account as well as arbitrary optical axis orientation and angle of incidence.Comment: 20 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-