相关论文: Monge Distance between Quantum States

Distance measures are indispensable tools in quantum information processing and quantum computing. This since they can be used to quantify to what extent information is preserved, or altered, by quantum processes. In this paper we propose a…

We look for upper bounds of the relative energy difference of two pure quantum states with a fixed fidelity between them or upper bounds of the fidelity for a fixed relative energy difference. The results depend on the concrete families of…

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…

We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…

Quantum fidelity is a central tool in quantum information, quantifying how much two quantum states are similar. Here we propose a limit formula for the quantum fidelity between a mixed state and a pure state. As an example of an…

We give sufficient conditions for a finite metric space to be determined by the magnitude function. In particular, a generic finite metric space such that the distances between the points are rationally independent is determined by the…

We introduce a measure of the compatibility between quantum states--the likelihood that two density matrices describe the same object. Our measure is motivated by two elementary requirements, which lead to a natural definition. We list some…

It is known that a reliable geometric quantifier of discord-like correlations can be built by employing the so-called trace distance. This is used to measure how far the state under investigation is from the closest "classical-quantum" one.…

We derive several bounds on fidelity between quantum states. In particular we show that fidelity is bounded from above by a simple to compute quantity we call super--fidelity. It is analogous to another quantity called sub--fidelity. For…

We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this…

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…

Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank at most k. This problem has already been solved when…

We define a new measure of quantum correlations in bipartite quantum systems given by the Bures distance of the system state to the set of classical states with respect to one subsystem, that is, to the states with zero quantum discord. Our…

The classical information metric provides a unique notion of distance on the space of probability distributions with a well-defined operational interpretation: two distributions are far apart if they are readily distinguishable from one…

We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than…

We discuss some basic tools for an analysis of one-dimensionalquantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states are reviewed. These states are then…

Quantum coherence and non-classical correlation are key features of quantum world. Quantifying coherence and non-classical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum…

We propose a measure of entanglement that can be computed for any pure state of an $M$-qubit system. The entanglement measure has the form of a distance that we derive from an adapted application of the Fubini-Study metric. This measure is…

The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon…

We show that there is genuine quantum chaos despite that quantum dynamics is linear. This is revealed by introducing a physical distance between two quantum states. Qualitatively different from existing distances for quantum states, for…