Related papers: Smooth Renyi Entropies and the Quantum Information…
The information spectrum approach gives general formulae for optimal rates of codes in many areas of information theory. In this paper the quantum spectral divergence rates are defined and properties of the rates are derived. The entropic…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
Quantum processes can exhibit scenarios beyond a fixed order of events. We propose information inequalities that, when violated, constitute sufficient conditions to certify quantum processes without a fixed causal order -- causally…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…
Signal processing and Information theory are two disparate fields used for characterizing signals for various scientific and engineering applications. Spectral/Fourier analysis, a technique employed in signal processing, helps estimation of…
We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…
We explore a recently introduced quantum thermodynamic entropy $S^Q_{univ}$ of a pure state of a composite system-environment computational "universe" with a simple system $\mathcal{S}$ coupled to a constant temperature bath $\mathcal{E}$.…
Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…
It is pointed out that the case for Shannon entropy and von Neumann entropy, as measures of uncertainty in quantum mechanics, is not as bleak as suggested in quant-ph/0006087. The main argument of the latter is based on one particular…
For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on…
Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we…
Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more…
We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…
This paper is the part-II of the previous paper and introduces the world of Yuen's concept. In the theory of cryptology, the Shannon impossibility theorem states that the upper bound of the security of a plaintext against a ciphertext-only…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…