Related papers: On the metric character of the quantum Jensen-Shan…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
Quantifying of quantum coherence of a given system not only plays an important role in quantum information science but also promote our understanding on some basic problems, such as quantum phase transition. Conventional quantum coherence…
Entangled states of pseudoscalar mesons represent a very interesting tool for studying foundations of quantum mechanics, e.g. for testing Bell inequalities. Recently, they also emerged as a test bench for quantum information protocols. On…
With the help of a given distance matrix of size $n$, we construct an infinite family of distances $d_p$ (where $p \geq 2$) on the complex projective space $\mathbb{P}(\mathbb{C}^n)$ modelling the space of pure states of an $n$-level…
The original definition of quantum discord of bipartite states was defined over one-sided projective measurements, it describes quantum correlation more extensively than entanglement. Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010)…
We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this…
A generic model of measurement device which is able to directly measure commonly used quantum-state characteristics such as fidelity, overlap, purity and Hilbert-Schmidt distance for two general uncorrelated mixed states is proposed. In…
Recently, trace distance measure of coherence has been proposed for characterizing the coherence of a given quantum state. However, it seems difficult to estimate the optimal incoherent state for high dimensional states. An explicit…
Radhakrishnan et.al [Phys. Rev. Lett. 124, 110401 (2020)] proposed a generalization of quantum discord to multipartite systems, which is consistency with the conventional definition of discord in bipartite systems and derived explicit…
We prove certain type symmetric inequalities in $\textbf{R}^{2}$ and $\textbf{R}^3$, that ocur in many problems of analysis. These inequalities are generalizations of the Jensen's inequality from one variable to two and three variables
Metrization of statistical divergences is valuable in both theoretical and practical aspects. One approach to obtaining metrics associated with divergences is to consider their fractional powers. Motivated by this idea, Os\'an, Bussandri,…
In quantum mechanics, geometry has been demonstrated as a useful tool for inferring non-classical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the…
In this paper we have considered two one parametric generalizations. These two generalizations have in articular the well known measures such as: J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric mean divergence. These three…
A geometric understanding of entanglement is proposed based on local measurements. Taking recourse to the general structure of density matrices in the framework of Euclidean geometry, we first illustrate our approach for bipartite Werner…
The Jensen-Shannon divergence is a renown bounded symmetrization of the Kullback-Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the…
We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…
The geometric measure of entanglement of a pure state, defined by its distance to the set of pure separable states, is extended to multipartite mixed states. We characterize the nearest disentangled mixed state to a given mixed state with…
Originally introduced as the difference between two possible forms of quantum mutual information, quantum discord has posteriorly been shown to admit a formulation according to which it measures a distance between the state under scrutiny…
The concept of quantum discord aims at unveiling quantum correlations that go beyond those described by entanglement. Its original formulation [J. Phys. A 34, 6899 (2001); Phys. Rev. Lett 88, 017901 (2002)] is difficult to compute even for…
In this paper, we systematically establish the mathematical foundation for the $\text{U}^N(1)$ quantum geometric tensor (QGT) of mixed states Explicitly, we present a description based on the $\text{U}^N(1)$ principal bundle and derive a…