相关论文: Quantum Wasserstein distance of order 1 between ch…
We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposal recovers the Hamming distance for the vectors of the canonical basis, and more generally the classical Wasserstein distance…
Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the $p$-Wasserstein distance, which serves to quantify the cost of transporting one probability…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
We define the quantum Wasserstein distance such that the optimization of the coupling is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that the…
Quantum Wasserstein divergences are modified versions of quantum Wasserstein distances defined by channels, and they are conjectured to be genuine metrics on quantum state spaces by De Palma and Trevisan. We prove triangle inequality for…
We propose a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice $\mathbb{Z}^d$, which we call specific quantum $W_1$ distance. The proposal is based on the $W_1$ distance for qudits of [De Palma et…
We introduce a non-quadratic generalization of the quantum mechanical optimal transport problem introduced in [De Palma and Trevisan, Ann. Henri Poincar\'e, {\bf 22} (2021), 3199-3234] where quantum channels realize the transport. Relying…
We study a class of quadratic Wasserstein distances on spaces consisting of generalized dynamical systems on a von Neumann algebra. We emphasize how symmetry of such a Wasserstein distance arises, but also study the asymmetric case. This…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
We develop a general approach to setting up and studying classes of quantum dynamical systems close to and structurally similar to systems having specified properties, in particular detailed balance. This is done in terms of transport plans…
In this note, we propose an extension of the Wasserstein 1-metric ($W_1$) for matrix probability densities, matrix-valued density measures, and an unbalanced interpretation of mass transport. The key is using duality theory, in particular,…
Optimal transport between classical probability distributions has been proven useful in areas such as machine learning and random combinatorial optimization. Quantum optimal transport, and the quantum Wasserstein distance as the minimal…
We propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a transport cost. Our proposal is the first where the transport…
Distinguishing quantum states with minimal sampling overhead is of fundamental importance to teach quantum data to an algorithm. Recently, the quantum Wasserstein distance emerged from the theory of quantum optimal transport as a promising…
We seek an analog for the quantum permutation group $S_n^+$ of the normalized Hamming distance for permutations. We define three distances on the tracial state space of $C(S_n^+)$ that generalize the $L^1$-Wasserstein distance of…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions $F$ and $G$ on $\mathbb R$. The estimator is based on the order statistics of (possibly dependent)…
In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant…
In this paper we study isometries of quantum Wasserstein distances and divergences on the quantum bit state space. We describe isometries with respect to the symmetric quantum Wasserstein divergence $d_{sym}$, the divergence induced by all…
Quadratic Wasserstein distances are obtained between dynamical systems (with states as special case), on $\mathbb{Z}_2$-graded von Neumann algebras. This is achieved through a systematic translation from non-graded to $\mathbb{Z}_2$-graded…