Related papers: Quantum Data Compression and Relative Entropy Revi…
The von Neumann entropy plays a vital role in quantum information theory. The von Neumann entropy determines, e.g., the capacities of quantum channels. Also, entropies of composite quantum systems are important for future quantum networks,…
Computational entropies provide a framework for quantifying uncertainty and randomness under computational constraints. They play a central role in classical cryptography, underpinning the analysis and construction of primitives such as…
It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…
I compare the role of the information in the classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the…
The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a…
By defining information entropy in terms of probabilities densities $|\Psi|^2$ ($\Psi$ is a wave function in the coordinate representation) it is explicitly shown how a loss of quantum information occurs in a transition from a quantum to a…
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…
It has been shown recently that the framework of quantum sampling, as introduced by Bouman and Fehr, can lead to new entropic uncertainty relations highly applicable to finite-key cryptographic analyses. Here we revisit these so-called…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
Deriving formulations for computing and estimating tight worst-case size increases for conjunctive queries with various constraints has been at the core of theoretical database research. If the problem has no constraints or only one…
When a measurement is made on a quantum system in which classical information is encoded, the measurement reduces the observers average Shannon entropy for the encoding ensemble. This reduction, being the {\em mutual information}, is always…
This research explores the integration of quantum data embedding techniques into classical machine learning (ML) algorithms, aiming to assess the performance enhancements and computational implications across a spectrum of models. We…
We address the problem of quantifying the information content of a source for an arbitrary information theory, where the information content is defined in terms of the asymptotic achievable compression rate. The functions that solve this…
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…
We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…
We have proven that there exists a quantum state approximating any multi-copy state universally when we measure the error by means of the normalized relative entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE Trans.…
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this…
Quantum networks play a key role in many scenarios of quantum information theory. Here we consider the quantum causal networks in the manner of entropy. First we present a revised smooth max-relative entropy of quantum combs, then we…