Related papers: Optimized quantum f-divergences and data processin…
The quantum relative entropy $S(\rho||\sigma)$ is a widely used dissimilarity measure between quantum states, but it has the peculiarity of being asymmetric in its arguments. We quantify the amount of asymmetry by providing a sharp upper…
Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…
Optimized quantum $f$-divergence was first introduced by Wilde in \cite{Wil18}. Wilde raised the question of whether the monotonicity of optimized quantum $f$-divergence can be generalized to maps that are not quantum channels. We answer…
Quantum state discrimination is a fundamental concept in quantum information theory, which refers to a class of techniques to identify a specific quantum state through a positive operator-valued measure. In this work, we investigate how…
We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…
A key component of a quantum machine learning model operating on classical inputs is the design of an embedding circuit mapping inputs to a quantum state. This paper studies a transfer learning setting in which classical-to-quantum…
We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this…
Recently, a new definition for quantum $f$-divergences was introduced based on an integral representation. These divergences have shown remarkable properties, for example when investigating contraction coefficients under noisy channels. At…
Quantum machine learning seeks a computational advantage in data processing by evaluating functions of quantum states, such as their similarity, that can be classically intractable to compute. For quantum advantage to be possible, however,…
We study a doubly minimized variant of the lautum information - a reversed analogue of the mutual information - defined as the minimum relative entropy between any product state and a fixed bipartite quantum state; we refer to this measure…
We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter,…
Federated Learning (FL) enables collaborative model training across distributed devices while preserving data privacy. Nonetheless, the heterogeneity of edge devices often leads to inconsistent performance of the globally trained models,…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
We give a new characterization of relative entropy, also known as the Kullback-Leibler divergence. We use a number of interesting categories related to probability theory. In particular, we consider a category FinStat where an object is a…
In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…
Inequality measures provide a valuable tool for the analysis, comparison, and optimization based on system models. This work studies the relation between attributes or features of an individual to understand how redundant, unique, and…
This paper is focused on derivations of data-processing and majorization inequalities for $f$-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…
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…