Related papers: Defining quantum divergences via convex optimizati…
Discriminating between noisy quantum processes is a central primitive for quantum communication, metrology, and computing. While discrimination limits for finite-dimensional channels are well understood, the continuous-variable setting,…
Maximal quantum $f$-divergences, defined via the commutant Radon--Nikodym derivative, form a fundamental class of distinguishability measures for quantum states associated with operator convex functions. In this paper, we study the…
We present a new random walk for uniformly sampling high-dimensional convex bodies. It achieves state-of-the-art runtime complexity with stronger guarantees on the output than previously known, namely in R\'enyi divergence (which implies…
This paper investigates three closely related topics -- R\'enyi resolvability, noise stability, and anti-contractivity. The R\'enyi resolvability problem refers to approximating a target output distribution of a given channel in the R\'enyi…
A set of classical or quantum states is equivalent to another one if there exists a pair of classical or quantum channels mapping either set to the other one. For dichotomies (pairs of states), this is closely connected to (classical or…
Gradient descent algorithms on Riemannian manifolds have been used recently for the optimization of quantum channels. In this contribution, we investigate the influence of various regularization terms added to the cost function of these…
Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to…
Quantum neural networks (QNNs) are a framework for creating quantum algorithms that promises to combine the speedups of quantum computation with the widespread successes of machine learning. A major challenge in QNN development is a…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
The present paper studies an operator norm that captures the distinguishability of quantum strategies in the same sense that the trace norm captures the distinguishability of quantum states or the diamond norm captures the…
Divergences, also known as contrast functions, are distance-like quantities defined on manifolds of non-negative or probability measures. Using the duality in optimal transport, we introduce and study the one-parameter family of $L^{(\pm…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…
Difference-of-Convex Algorithm (DCA) is a well-known nonconvex optimization algorithm for minimizing a nonconvex function that can be expressed as the difference of two convex ones. Many famous existing optimization algorithms, such as SGD…
The measured relative entropy and measured R\'enyi relative entropy are quantifiers of the distinguishability of two quantum states $\rho$ and $\sigma$. They are defined as the maximum classical relative entropy or R\'enyi relative entropy…
R\'enyi divergence is related to R\'enyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
Recently, the projective robustness of quantum states has been introduced in [arXiv:2109.04481(2021)]. It shows that the projective robustness is a useful resource monotone and can comprehensively characterize capabilities and limitations…
Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are…
Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we…