Related papers: Sampling of min-entropy relative to quantum knowle…
The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any…
The extraction of randomness from weakly random seeds is a problem of central importance with multiple applications. In the device-independent setting, this problem of quantum randomness amplification has been mainly restricted to specific…
Importance sampling of target probability distributions belonging to a given convex class is considered. Motivated by previous results, the cost of importance sampling is quantified using the relative entropy of the target with respect to…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
We present full generalisations of entropic security and entropic indistinguishability to the quantum world where no assumption but a limit on the knowledge of the adversary is made. This limit is quantified using the quantum conditional…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
In classical physics, entropy quantifies the randomness of large systems, where the complete specification of the state, though possible in theory, is not possible in practice. In quantum physics, despite its inherently probabilistic…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
Compact expressions for the average subentropy and coherence are obtained for random mixed states that are generated via various probability measures. Surprisingly, our results show that the average subentropy of random mixed states…
An extractor is a function E that is used to extract randomness. Given an imperfect random source X and a uniform seed Y, the output E(X,Y) is close to uniform. We study properties of such functions in the presence of prior quantum…
Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy,…
We investigate optimal encoding and retrieval of digital data, when the storage/communication medium is described by quantum mechanics. We assume an m-ary alphabet with arbitrary prior distribution, and an n-dimensional quantum system.…
The Rains relative entropy of a bipartite quantum state is the tightest known upper bound on its distillable entanglement -- which has a crisp physical interpretation of entanglement as a resource -- and it is efficiently computable by…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
Given a sequence composed of a limit number of characters, we try to "read" it as a "text". This involves to segment the sequence into "words". The difficulty is to distinguish good segmentation from enormous number of random ones.Aiming at…
We consider an extension of the conditional min- and max-entropies to infinite-dimensional separable Hilbert spaces. We show that these satisfy characterizing properties known from the finite-dimensional case, and retain…
Dependence among marginally constrained observations can break a finite-sample barrier. To formalize this phenomenon, we introduce the \emph{minimum list entropy coupling} $H(P\|Q_1,\dots,Q_m)$, the minimum conditional entropy…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
The leakage chain rule for quantum min-entropy quantifies the change of min-entropy when one party gets additional leakage about the information source. Herein we provide an interactive version that quantifies the change of min-entropy…