Related papers: Discontinuities in the Maximum-Entropy Inference
We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…
The concept of Relative Divergence of one Grading Function from another is extended from totally ordered chains to power sets of finite event spaces. Shannon Entropy concept is extended to normalized grading functions on such power sets.…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
The science of cities is a relatively new and interdisciplinary topic. It borrows techniques from agent-based modeling, stochastic processes, and partial differential equations. However, how the cities rise and fall, how they evolve, and…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…
Quantum theory allows for the superposition of causal orders between operations, i.e., for an indefinite causal order; an implication of the principle of quantum superposition. Since a higher theory might also admit this feature, an…
The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…
Consider the set of all sequences of $n$ outcomes, each taking one of $m$ values, that satisfy a number of linear constraints. If $m$ is fixed while $n$ increases, most sequences that satisfy the constraints result in frequency vectors…
The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to…
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…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
The main goal of this paper is to extend and apply the principle of maximum entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define a so-called process entropy function being the von Neumann entropy of the state…
As data plays an increasingly pivotal role in decision-making, the emergence of data markets underscores the growing importance of data valuation. Within the machine learning landscape, Data Shapley stands out as a widely embraced method…
Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…
Started from local universal isotropic disentanglement, a threshold inequality on reduction factors is proposed, which is necessary and sufficient for this type of disentanglement processes. Furthermore, we give the conditions realizing…
We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the…
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…
This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are…