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Despite their elegance and widespread use, the current Geometric Measures (GMs) of entanglement exhibit a significant limitation: they fail to effectively distinguish Local Unitary (LU) inequivalent states due to the inherent nature of their definition. We illustrate the impact of this limitation using the fidelity of the teleportation protocol as an example. To address this issue, we introduce the Sharp Geometric Measure (SGM) by modifying the standard definition of the Geometric Measure. We show that the closed-form expression of the SGM can be equivalently derived using the Riemannian structure of both the composite state space and the reduced density operator space. Furthermore, we define a measure of Genuine Multipartite Entanglement (GME) derived from the SGM, which we term GMS. We demonstrate that GMS resolves two key limitations of some existing GME measures, thereby establishing its utility and effectiveness in quantifying GME., Comment: Comments are welcome

We introduce an entanglement measure, the Modified Bloch Norm ($MBN$), for finite-dimensional bipartite mixed states, based on the improved Bloch matrix criteria. $MBN$ is demonstrated to be effective in analyzing the dynamics of bound entanglement--a valuable resource for quantum protocols where free entanglement may not be available. Through examples, we illustrate the applications of $MBN$ in accurately estimating the Entanglement Sudden Death (ESD) time and detecting behaviour such as the freezing of bound entanglement. Additionally, we show that the error rate for entanglement measured using state estimation from a limited number of measurement copies is significantly lower when using $MBN$ compared to negativity. This demonstrates the robustness of $MBN$ under practical constraints., Comment: Comments are welcome

Emergence of classicality from quantum mechanics, a hotly debated topic, has had no satisfactory resolution so far. Various approaches including decoherence and gravitational interactions have been suggested. In the present work, the Schr\"odinger-Newton model is used to study the role of semi-classical self-gravity in the evolution of massive spin-1/2 particles in a Stern-Gerlach experiment. For small mass, evolution of the initial wavepacket in a spin superposition shows a splitting in the magnetic field gradient into two trajectories as in the standard Stern-Gerlach experiment. For larger mass, the deviations from the central path are less than in the standard Stern-Gerlach case, while for high enough mass, the wavepacket does not split, and instead follows the classical trajectory for a magnetic moment in inhomogeneous magnetic field. This indicates the emergence of classicality due to self-gravitational interaction when the mass is increased. In contrast, decoherence which is a strong contender for emergence of classicality, leads to a \emph{mixed state} of two trajectories corresponding to the spin-up and spin-down states, and not the classically expected path. The classically expected path of the particle probably cannot be explained even in the many-worlds interpretation of quantum mechanics. Stern-Gerlach experiments in the macroscopic domain are needed to settle this question., Comment: To appear in Annalen der Physik

While several measures exist for entanglement of multipartite pure states, a true entanglement measure for mixed states still eludes us. A deeper study of the geometry of quantum states may be the way to address this issue, on which context we come up with a measure for pure states based on a geodesic distance on the space of quantum states. Our measure satisfies all the desirable properties of a ``Genuine Measure of Entanglement" (GME), and in comparison with some of the other existing measures, shows better smoothness and discriminance., Comment: This work was not complete and had some incorrect assumptions as it was pointed out by a few peers. An impoved version of ideas used here are presented as Sharp Geometric Measure

The Schrodinger-Newton equation has frequently been studied as a nonlinear modification of the Schrodinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on interference of massive particles is studied by numerically solving the Schrodinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on the fringe width of the interference that can be tested in matter-wave interferometry experiments. Notably, this approach can distinguish between gravitational self-interaction and environment induced decoherence, as the latter does not affect the fringe width. This result will also provide a way to test if gravity requires to be quantized on the scale of ordinary quantum mechanics., Comment: 8 pages, 6 figures, throughly revised and expanded

The two-slit experiment with quantum particles provides many insights into the behaviour of quantum mechanics, including Bohr's complementarity principle. Here we analyze Einstein's recoiling slit version of the experiment and show how the inevitable entanglement between the particle and the recoiling slit as a which-way detector is responsible for complementarity. We derive the Englert-Greenberger-Yasin duality from this entanglement, which can also be thought of as a consequence of sum-uncertainty relations between certain complementary observables of the recoiling slit. Thus, entanglement is an integral part of the which-way detection process, and so is uncertainty, though in a completely different way from that envisaged by Bohr and Einstein., Comment: 7 pages, RevTeX. Closest to the published version

We analyze Einstein's recoiling slit experiment and point out that the inevitable entanglement between the particle and the recoiling-slit was not part of Bohr's reply. We show that if this entanglement is taken into account, one can provided a simpler answer to Einstein. We also derive the Englert-Greenberger-Yasin duality relation from this entanglement. In addition, we show that the Englert-Greenberger-Yasin duality relation can also be thought of as a consequence of the sum uncertainty relation for certain observables of the recoiling slit. Thus, the uncertainty relations and entanglement are both an integral part of the which-way detection process., Comment: 7 pages, closest to the published version

We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for arbitrary number of anyons, a subset of exact solutions which may be interpreted as the breathing modes or equivalently collective modes of the full system. Choosing the three-anyon system as an example, we also discuss the anatomy of the so called ``missing'' states which are in fact known numerically and are set apart from the known exact states by their nonlinear dependence on the statistical parameter in the spectrum. Though classically the equations of motion remains unchanged in the presence of the statistical interaction, the system is non-integrable because the configuration space is now multiply connected. In fact we show that even though the number of constants of motion is the same as the number of degrees of freedom the system is in general not integrable via action-angle variables. This is probably the first known example of a many body pseudo-integrable system. We discuss the classification of the orbits and the symmetry reduction due to the interaction. We also sketch the application of periodic orbit theory (POT) to many anyon systems and show the presence of eigenvalues that are potentially non-linear as a function of the statistical parameter. Finally we perform the semiclassical analysis of the ground state by minimizing the Hamiltonian with fixed angular momentum and further minimization over the quantized values of the angular momentum., Comment: 44 pages, one figure, eps file. References updated

We study soliton solutions in supersymmetric scalar field theory with a class of potentials. We study both bosonic and fermionic zero-modes around the soliton solution. We study two possible couplings of gauge fields to these models. While the Born-Infeld like coupling has one normalizable mode (the zero mode), the other kind of coupling has no normalizable modes. We show that quantum mechanical problem which determines the spectrum of fluctuation modes of the scalar, fermion and the gauge field is identical. We also show that only the lowest lying mode, i.e., the zero mode, is normalizable and the rest of the spectrum is continuous., Comment: 10 pages, 2 figures, LaTeX

We study soliton solutions in scalar field theory with a variety of unbounded potentials. A subset of these potentials have Gaussian lump solutions and their fluctuation spectrum is governed by the harmonic oscillator problem. These lumps are unstable with one tachyonic mode. Soliton solutions in several other classes of potentials are stable and are of kink type. The problem of the stability of these solutions is related to a supersymmetric quantum mechanics problem. The fluctuation spectrum is not equispaced and does not contain any tachyonic mode. The lowest energy mode is the massless Goldstone mode which restores broken translation invariance., Comment: Latex, 13 pages, 3 figures; references updated

The two-dimensional anyon system, when reduced to one dimension, yields models related to the Calogero-Sutherland model. One such reduction leads to a new model with a class of exact solutions. This model is one of a family of models obtained upon dimensional reduction of spherically symmetric models in arbitrary dimensions., Comment: 12 pages, no Figures, to appear in IJMP A

We report on a study of a classical, finite system of confined particles in two dimensions with a two-body repulsive interaction. We first develop a simple analytical method to obtain equilibrium configurations and energies for few particles. When the confinement is harmonic, we prove that the first transition from a single shell occurs when the number of particles changes from five to six. The shell structure in the case of an arbitrary number of particles is shown to be independent of the strength of the interaction but dependent only on its functional form. It is also independent of the magnetic field strength when included. We further study the effect of the functional form of the confinement potential on the shell structure. Finally we report some interesting results when a three-body interaction is included, albeit in a particular model., Comment: Minor corrections, a few references added. To appear in J. Phys: Condensed Matter

The methods of reduced phase space quantization and Dirac quantization are examined in a simple gauge theory. A condition for the possible equivalence of the two methods is discussed., Comment: 8 pages. RevTex (two-column), no figures. The dvi version can be downloaded from: http://www.imsc.ernet.in/physweb/papers/radhika/pa2.dvi