相关论文: Layer Cake Representations for Quantum Divergences

A theorem by Orlov states that any equivalence between the bounded derived categories of coherent sheaves of two smooth projective varieties, X and Y, is isomorphic to a Fourier-Mukai transform with kernel in the bounded derived category of…

We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of the space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for…

In this paper we deal with two quantum relative entropy preserver problems on the cones of positive (either positive definite or positive semidefinite) operators. The first one is related to a quantum R\'enyi relative entropy like quantity…

Steinberg's tensor product theorem shows that for semisimple algebraic groups the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the…

Quantum relative entropy, a quantum generalization of the renowned Kullback-Leibler divergence, serves as a fundamental measure of the distinguishability between quantum states and plays a pivotal role in quantum information science.…

The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…

A new sharp inequality featuring the differential R\'enyi entropy, the R\'enyi divergence and the R\'enyi cross-entropy of a pair of probability density functions is established. The equality is reached when one of the probability density…

We consider multi-layered cake cutting in order to fairly allocate numerous divisible resources (layers of cake) among a group of agents under two constraints: contiguity and feasibility. We first introduce a new computational model in a…

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 provide a transparent, simple and unified treatment of recent results on the equality conditions for the data processing inequality (DPI) of the sandwiched quantum R\'enyi divergence, including the statement that equality in the data…

Quantum coherence is a crucial resource for quantum information processing. By employing the language of coherence orders largely applied in NMR systems, quantum coherence has been currently addressed in terms of multiple quantum coherences…

In the problem of binary quantum channel discrimination with product inputs, the supremum of all type II error exponents for which the optimal type I errors go to zero is equal to the Umegaki channel relative entropy, while the infimum of…

Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…

We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the…

We propose an extension of the classical R\'enyi divergences to quantum states through an optimization over probability distributions induced by restricted sets of measurements. In particular, we define the notion of locally-measured…

Phase-space versions of quantum mechanics -- from Wigner's original distribution to modern discrete-qudit constructions -- represent some states with negative quasi-probabilities. Conventional Shannon and R\'enyi entropies become…

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…

We examine the logical difficulties that arise when a particle(wave) interferes with itself. We propose to carry out to its full extent a `gedanken' experiment originally proposed by Feynman in order to give an unequivocal experimental…

Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…