Related papers: Comparing computational entropies below majority (…
It is believed that the more we have {\it a priori} information on input states, the better we can make the quality of clones in quantum cloning machines. This common sense idea was confirmed several years ago by analyzing a situation,…
The similarity of local atomic environments is an important concept in many machine-learning techniques which find applications in computational chemistry and material science. Here, we present and discuss a connection between the…
We introduce hardness in relative entropy, a new notion of hardness for search problems which on the one hand is satisfied by all one-way functions and on the other hand implies both next-block pseudoentropy and inaccessible entropy, two…
A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead,…
Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or…
Communication of quantized information is frequently followed by a computation. We consider situations of \emph{distributed functional scalar quantization}: distributed scalar quantization of (possibly correlated) sources followed by…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
A coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse…
A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers,…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
In this work, we develop a generalisation of the thermal entropy to complex inverse temperatures, which we call the thermal pseudo-entropy. We show that this quantity represents the pseudo-entropy of the transition matrix between…
We prove various extensions of the Tennenbaum phenomenon to the case of computable quotient presentations of models of arithmetic and set theory. Specifically, no nonstandard model of arithmetic has a computable quotient presentation by a…
Since the work of Ferrenberg et al.[PRL 69, (1992)] some pseudo random number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed.…
The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of measuring the von Neumann entropy, $S(\rho)$, and R\'enyi entropy, $S_\alpha(\rho)$ of an…
We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…