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Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
In this work, we prove a lower bound on the difference between the first and second singular values of quantum channels induced by random isometries, that is tight in the scaling of the number of Kraus operators. This allows us to give an…
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
We show that under a certain condition of local commutativity the minimum von-Neumann entropy output of a quantum channel is locally additive. We also show that local minima of the 2-norm entropy functions are closed under tensor products…
We present a machine learning framework to study the dynamics of entropy vectors and quantum resources, including entanglement and magic, focusing on violations of entropy inequalities. Using a reinforcement learning agent formulated as a…
We address in this work the problem of minimizing quantum entropies under local constraints. We suppose macroscopic quantities such as the particle density, current, and kinetic energy are fixed at each point of $\Rm^d$, and look for a…
A longstanding open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding…
Determining the ultimate limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state, remains a central challenge in quantum information theory, primarily due to the…
We study the vanishing-regularization limit of entropically regularized optimal transport (EOT) for the Euclidean distance cost $c(x,y)=\|x-y\|$ in dimension $d>1$. We develop a comprehensive variational convergence framework that entails…
Important quantum algorithm routines allow the implementation of specific quantum operations (a.k.a. gates) by combining basic quantum circuits with an iterative structure. In this structure, the number of repetitions of the basic circuit…
Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements…
This paper presents self-contained proofs of the strong subadditivity inequality for quantum entropy and some related inequalities for the quantum relative entropy, most notably its convexity and its monotonicity under stochastic maps.…
We propose an approach to the study of quantum resource manipulation based on the basic observation that quantum channels which preserve certain sets of states are contractive with respect to the base norms induced by those sets. We forgo…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
Relative entropy is the standard measure of distinguishability in classical and quantum information theory. In the classical case, its loss under channels admits an exact chain rule, while in the quantum case only asymptotic, regularized…
Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in any non-contextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of…
In this paper, we compute the exact values of the minimum output entropy and the completely bounded minimal entropy of very large classes of quantum channels acting on matrix algebras $\mathrm{M}_n$. Our new and simple approach relies on…
In a breakthrough, Hastings' showed that there exist quantum channels whose classical capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as…
New quantum entropic inequality for states of system of n >_ 1 qudits is obtained. The inequality has the form of quantum subadditivity condition of bipartite qudit system and coincides with this subadditivity condition for the system of…