Related papers: Quantum optimal transport with quantum channels
We propose a new formulation of the Wigner transport equation with infinite correlation length. Since the maximum correlation length is not limited to a finite value, there is no uncertainty in the simulation results owing to the finite…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
In this paper we introduce a new partial order on quantum states that considers which states can be achieved from others by updating on `agreeing' Bayesian evidence. We prove that this order can also be interpreted in terms of minimising…
In contrast to discrete-variable teleportation, a quantum state is imperfectly transferred from a sender to a remote receiver in a continuous-variable setting. We recall the ingenious scheme proposed by Braunstein and Kimble for teleporting…
We study the Braunstein-Kimble setup for teleportation of quantum state of a single mode of optical field. We assume that the sender and receiver share a two-mode Gaussian state and we identify optimum local Gaussian operations that…
Constructing optimal thermodynamic processes in quantum systems relies on managing the balance between the average excess work and its stochastic fluctuations. Recently it has been shown that two different quantum generalisations of…
We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the optimal strategy that minimizes the total probability of error. This leads to the identification of the…
Quantum communication is an important branch of quantum information science, promising unconditional security to classical communication and providing the building block of a future large-scale quantum network. Noise in realistic quantum…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
In this paper, we propose a novel quantum computing approach to solve the real-world problem of optimizing transportation in bustling Kathmandu city. The transportation system in Kathmandu is chaotic, with no central authority controlling…
We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…
We study quantum neural networks where the generated function is the expectation value of the sum of single-qubit observables across all qubits. In [Girardi \emph{et al.}, arXiv:2402.08726], it is proven that the probability distributions…
In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Euler discretization…
Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two quantum nodes. All bidirectional quantum teleportation protocols till now have achieved a maximum efficiency of $40\%$. Here, we…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension. We prove that any such Gibbs state which satisfies a clustering condition that we coin…
Overlap-based distinguishability measures, such as fidelity- or Chernoff-type quantities, play a central role in quantum sensing and quantum illumination. In strongly lossy and fluctuating environments, however, these quantities may become…