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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