相关论文: Quantum Wasserstein distance of order 1 between ch…
We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass. This generalization inherits the convexity and computational efficiency from the…
Optimal transport theory has recently been extended to quantum settings, where the density matrices generalize the probability measures. In this paper, we study the computational aspects of the order 2 quantum Wasserstein distance,…
Wasserstein distances provide a metric on a space of probability measures. We consider the space $\Omega$ of all probability measures on the finite set $\chi = \{1, \dots ,n\}$ where $n$ is a positive integer. 1-Wasserstein distance,…
Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…
The Quasi Manhattan Wasserstein Distance (QMWD) is a metric designed to quantify the dissimilarity between two matrices by combining elements of the Wasserstein Distance with specific transformations. It offers improved time and space…
Persistence diagrams are a useful tool from topological data analysis which can be used to provide a concise description of a filtered topological space. What makes them even more useful in practice is that they come with a notion of a…
Quantifying the effect of noise on unitary operations is an essential task in quantum information processing. We propose the quantum Wasserstein distance between unitary operations, which shows an explanation for quantum circuit complexity…
We consider several definitions of the quantum Wasserstein distance based on an optimization over general bipartite quantum states with given marginals. Then, we examine the quantities obtained after the optimization is carried out over…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…
We study the Wasserstein metric to measure distances between molecules represented by the atom index dependent adjacency "Coulomb" matrix, used in kernel ridge regression based supervised learning. Resulting quantum machine learning models…
We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…
Given a unitary transformation, what is the size of the smallest quantum circuit that implements it? This quantity, known as the quantum circuit complexity, is a fundamental property of quantum evolutions that has widespread applications in…
We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for…
We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are…
Generalized Wasserstein distances allow to quantitatively compare two continuous or atomic mass distributions with equal or different total mass. In this paper, we propose four numerical methods for the approximation of three different…
Given two rational univariate polynomials, the Wasserstein distance of their associated measures is an algebraic number. We determine the algebraic degree of the squared Wasserstein distance, serving as a measure of algebraic complexity of…
In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we…
These notes are based on the lectures given by the second author at the School on Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. The focus of the exposition is on two recently introduced approaches on quantum…
The quantum Wasserstein distances defined by Golse, Mouhot, Paul, and Caglioti and by De Palma and Trevisan coincide for qubits when a single operator appears in the cost function. As a consequence, the self-distance equals the…
The convergence rate in Wasserstein distance is estimated for the empirical measures of symmetric semilinear SPDEs. Unlike in the finite-dimensional case that the convergence is of algebraic order in time, in the present situation the…