Related papers: On the metric character of the quantum Jensen-Shan…
We advance a novel perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose an criterium based on the consideration of convex subsets of quantum states. This…
Fidelity plays an important role in measuring distances between pairs of quantum states, of single as well as multiparty systems. Based on the concept of fidelity, we introduce a physical quantity, shared purity, for arbitrary pure or mixed…
Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. Exact results are known only for very special states, namely,…
The quantumness of the correlation known as quantum correlation is usually measured by quantum discord. So far various quantum discords can be roughly understood as indirect measure by some special discrepancy of two quantities. We present…
We study the $\epsilon$-level sets of the signed distance function to a planar Jordan curve $\Gamma$, and ask what properties of $\Gamma$ ensure that the $\epsilon$-level sets are Jordan curves, or uniform quasicircles, or uniform chord-arc…
The scheme for construction of distances, presented in the previous paper quant-ph/0005087, v.1 (Ref. 1) is amended. The formulation of Proposition 1 of Ref. 1 does not ensure the triangle inequality, therefore some of the functionals…
Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It…
Vector similarity measures play a fundamental role in various fields, including machine learning, natural language processing, information retrieval, and data mining. These measures quantify the closeness between two vectors in a…
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively…
Especially investigated in recent years, the Gaussian discord can be quantified by a distance between a given two-mode Gaussian state and the set of all the zero-discord two-mode Gaussian states. However, as this set consists only of…
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated…
In this study, using the concept of relative entropy as a distance measure of cor- relations we investigate the important issue of evaluating quantum correlations such as entanglement, dissonance and classical correlations for…
We study quantum steering experiments without assuming that the trusted party can perfectly control their measurement device. Instead, we introduce a scenario in which these measurements are subject to small imprecision. We show that small…
Entanglement is a central feature of quantum theory. Mathematical properties and physical applications of pure state entanglement make it a template to study quantum correlations. However, an extension of entanglement measures to mixed…
When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric…
We set up a general theory for a quantum Wasserstein distance of order 1 in an operator algebraic framework, extending recent work in finite dimensions. In addition, this theory applies not only to states, but also to channels, giving a…
We study the problem of whether the curvature-dimension condition with negative values of the generalized dimension parameter is stable under a suitable notion of convergence. To this purpose, first of all we introduce an appropriate…
We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of…
In this work, we perform an in-depth study of recently introduced average-case quantum distances. The average-case distances approximate the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in…
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with…