arXiv subjects

S. Chaturvedi

Publications and source records attributed to S. Chaturvedi.

At least 19 recordsLinked to original sources

arXiv2021

Optimal quantum tomography with constrained elementary measurements arising from unitary bases

The purpose of this paper is to introduce techniques of obtaining optimal ways to determine a d-level quantum state or distinguish such states. It entails designing constrained elementary measurements extracted from maximal abelian subsets of a unitary basis U for the operator algebra B(H) of a Hilbert space H of finite dimension d > 3 or, after choosing an orthonormal basis for H, for the *-algebra Md of complex matrices of order d > 3. Illustrations are given for the techniques. It is shown that the Schwinger basis U of unitary operators can give for d, a product of primes p and a, the ideal number d^2 of rank one projectors that have a few quantum mechanical overlaps (or, for that matter, a few angles between the corresponding unit vectors). We also give a combination of the tensor product and constrained elementary measurement techniques to deal with all d. A comparison is drawn for different forms of unitary bases for the Hilbert space and also for different Hilbert space factors of the tensor product. In the process we also study the equivalence relation on unitary bases defined by R. F. Werner [J. Phys. A: Math. Gen. 34 (2001) 7081], connect it to local operations on maximally entangled vectors bases, find an invariant for equivalence classes in terms of certain commuting systems, called fan representations, and, relate it to mutually unbiased bases and Hadamard matrices. Illustrations are given in the context of latin squares and projective representations as well.

quant-ph↗

arXiv2020

Properties of Spin and Orbital Angular Momenta of Light

This paper analyzes the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre--Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.

quant-ph↗

arXiv2020

Symplectic group methods and the Arthurs Kelly model of measurement in quantum mechanics

We study the use of methods based on the real symplectic groups $Sp(2n,\mathcal{R})$ in the analysis of the Arthurs-Kelly model of proposed simultaneous measurements of position and momentum in quantum mechanics. Consistent with the fact that such measurements are in fact not possible, we show that the observable consequences of the Arthurs-Kelly interaction term are contained in the symplectic transformation law connecting the system plus apparatus variance matrices at an initial and a final time. The individual variance matrices are made up of averages and spreads or uncertainties for single hermitian observables one at a time, which are quantum mechanically well defined. The consequences of the multimode symplectic covariant Uncertainty Principle in the Arthurs-Kelly context are examined.

quant-ph↗

arXiv2018

Geometric Phase as the Key to Interference in Phase Space : Integral Representations for States and Matrix Elements

We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths, phase space interference turns out to be determined by areas. The motivating idea is Pancharatnam's concept of "being in phase" for Hilbert space vectors. Applied to the overcomplete family of coherent states, we are led to preferred one-dimensional integral representations for various states of physical significance, such as the position, momentum, Fock states and the squeezed vacuum. These are special in the sense of being "in-phase superpositions". Area considerations emerge naturally within a fully quantum mechanical context. Interestingly, the Q-function is maximized along the line of such superpositions. We also get a fresh perspective on the Bohr-Sommerfeld quantization condition. Finally, we use our exact integral representations to obtain asymptotic expansions for state overlaps and matrix elements, leading to phase space area considerations similar to the ones noted earlier in the seminal works of Schleich, Wheeler and collaborators, but now from the perspective of geometric phase.

quant-ph↗

arXiv2017

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.

quant-ph↗

arXiv2017

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.

quant-ph↗

arXiv2017

Global aspects of polarization optics and coset space geometry

We use group theoretic ideas and coset space methods to deal with problems in polarization optics of a global nature. These include the possibility of a globally smooth phase convention for electric fields for all points on the Poincaré sphere, and a similar possibility of real or complex bases of transverse electric vectors for all possible propagation directions. It is shown that these methods help in understanding some known results in an effective manner, and in answering new questions as well. We find that apart from the groups $SU(2)$ and $SO(3)$ which occur naturally in these problems, the group $SU(3)$ also plays an important role.

physics.class-ph↗

arXiv2013

Classical Light Beams and Geometric Phases

We present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarisation optics, and the behaviour of polarisation in the eikonal or ray limit of Maxwell's equations in a transparent medium are considered. The case of a beam of light whose propagation direction and polarisation state are both subject to change is dealt with, attention being paid to the validity of Maxwell's equations at all stages. Global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas, and the effects on geometric phases are elucidated.

physics.optics↗

arXiv2013

Statistical comparison of quark mass matrices\\ in the physical basis

Using the four best measured moduli of the flavor mixing matrix ($|V_{\rm ud}|$, $|V_{\rm us}|$, $|V_{\rm cd}|$, $|V_{\rm cs}|$), the Jarlskog invariant $J(V)$, and the quark masses at $M_Z$ energy scale as experimental constraints, a statistical comparison of three different types of quark mass matrices in the physical basis is performed. The mass matrices in question are the Chaturvedi-Gupta-Sánchez-Colón (CGS), the Fritzsch and the Gupta-Rajpoot types. With nine parameters the best fits are obtained using a Gupta-Rajpoot type matrix while with seven parameters the best fits are obtained using the CGS type matrix. The stability of our analysis with respect to evolution of the quark masses is also presented.

hep-ph↗

arXiv2013

A quantum dynamical framework for Brownian heat engines

We present a self contained formalism modelled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines like Carnot, Stirling and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state enables permits us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyse in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and techniques and exactly solvable models presented here are interesting in their own right and, in our opinion, would find useful applications in other contexts as well.

quant-ph↗

arXiv2013

Null Phase Curves and Manifolds in Geometric Phase Theory

Bargmann invariants and null phase curves are known to be important ingredients in understanding the essential nature of the geometric phase in quantum mechanics. Null phase manifolds in quantum-mechanical ray spaces are submanifolds made up entirely of null phase curves, and so are equally important for geometric phase considerations. It is shown that the complete characterization of null phase manifolds involves both the Riemannian metric structure and the symplectic structure of ray space in equal measure, which thus brings together these two aspects in a natural manner.

quant-ph↗

arXiv2010

Entanglement and nonclassicality for multi-mode radiation field states

Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multi-mode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beamsplitters, in a transparent manner. For single mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beamsplitter, these conditions turn exactly into signatures of NPT entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two--mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beamsplitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three--mode beamsplitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.

quant-ph↗

arXiv2010

Recursive parametrization of Quark flavour mixing matrices

We examine quark flavour mixing matrices for three and four generations using the recursive parametrization of $U(n)$ and $SU(n)$ matrices developed by some of us in Refs.[2] and [3]. After a brief summary of the recursive parametrization, we obtain expressions for the independent rephasing invariants and also the constraints on them that arise from the requirement of mod symmetry of the flavour mixing matrix.

hep-ph↗

arXiv2009

Amplification of NOON States

We examine the behavior of a Non Gaussian state like NOON state under phase insensitive amplification. We derive analytical result for the density matrix of the NOON state for arbitrary gain of the amplifier. We consider cases of both symmetric and antisymmetric amplification of the two modes of the NOON state. We quantitatively evaluate the loss of entanglement by the amplifier in terms of the logarithmic negativity parameter. We find that NOON states are more robust than their Gaussian counterparts.

quant-ph↗

arXiv2009

How much quantum noise of amplifiers is detrimental to entanglement

We analyze the effect of the quantum noise of an amplifier on the entanglement properties of an input state. We consider both phase insensitive and phase sensitive amplification and specialize to Gaussian states for which entanglement measures are well developed. In the case of phase insensitive amplification in which both the modes are symmetrically amplified, we find that the entanglement in the output state vanishes if the intensity gain exceeds a limiting value $2/(1+\exp[-E_N])$ where $E_N$ is the logarithmic negativity of the input state which quantifies the initial entanglement between the two modes. The entanglement between the two modes at the output is found to be more robust if only one mode is amplified.

quant-ph↗

arXiv2009

Wigner distributions for finite state systems without redundant phase point operators

We set up Wigner distributions for $N$ state quantum systems following a Dirac inspired approach. In contrast to much of the work on this case, requiring a $2N\times 2N$ phase space, particularly when $N$ is even, our approach is uniformly based on an $N\times N $ phase space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both $N$ odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the $N$ 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.

quant-ph↗

arXiv2009

Entanglement Properties and Phase Diagram of the Two-Orbital Atomic Hubbard Model

We study the two-orbital Hubbard model in the limit of vanishing kinetic energy. The phase diagram in the $V-J$ plane, with $V$ and $J$ denoting the interorbital hybridization and exchange coupling respectively, at half filling is obtained. A singlet(dimer)-triplet transition is found for a critical value of the ratio $V/J.$ The entropy of formation, both in the mode and in the particle picture, presents a jump as the same critical line in conformity with the suggested relation between criticality and entanglement.

cond-mat.str-el↗

arXiv2009

Hamilton's theory of turns revisited

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.

quant-ph↗