Related papers: Mutual information challenges entropy bounds
This note will introduce some notation and definitions for information theoretic quantities in the context of quantum systems, such as (conditional) entropy and (conditional) mutual information. We will employ the natural C*-algebra…
Entanglement and information are powerful lenses to probe phases transitions in many-body systems. Motivated by recent cold atom experiments, which are now able to measure the corresponding information-theoretic quantities, we study the…
Overfitting data is a well-known phenomenon related with the generation of a model that mimics too closely (or exactly) a particular instance of data, and may therefore fail to predict future observations reliably. In practice, this…
The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a mixed density matrix with non zero entropy. This is usually called entanglement entropy, and it is known to be divergent in quantum…
We investigate the entropy bound for local quantum field theory in this paper. Both the bosonic and fermionic fields confined to an asymptotically flat spacetime are examined. By imposing the non-gravitational collapse condition, we find…
In the dynamics of open quantum systems, the backflow of information to the reduced system under study has been suggested as the actual physical mechanism inducing memory and thus leading to non-Markovian quantum dynamics. To this aim, the…
Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned…
An explicit calculation is given of the entropy/energy ratio for the TM modes of the electromagnetic field in the half Einstein universe. This geometry provides a mathematically convenient and physically instructive example of how the…
In a pair of recent articles [PRL 105 (2010) 041302 - arXiv:1005.1132; JHEP 1103 (2011) 056 - arXiv:1012.2867] two of the current authors have developed an entropy bound for equilibrium uncollapsed matter using only classical general…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic…
Mutual information I in infinite sequences (and in their finite prefixes) is essential in theoretical analysis of many situations. Yet its right definition has been elusive for a long time. I address it by generalizing Kolmogorov Complexity…
The AdS/CFT correspondence states an equivalence between a quantum gravitational theory in a (d+1)-dimensional anti-de Sitter spacetime (AdS$_{d+1}$) and a d-dimensional conformal field theory (CFT$_{d}$). The CFT$_{d}$ lives on the…
We use the notion of double holography to study Hawking radiation emitted by the eternal BTZ black hole in equilibrium with a thermal bath, but in the form of warped CFT$_2$ degrees of freedom. In agreement with the literature, we find…
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,…
In a quantum gravity theory the entropy of entanglement $S$ between the fundamental degrees of freedom spatially divided by a surface is discussed. The classical gravity is considered as an emergent phenomenon and arguments are presented…
The mutual information between two jointly distributed random variables $X$ and $Y$ is a functional of the joint distribution $P_{XY},$ which is sometimes difficult to handle or estimate. A coarser description of the statistical behavior of…
We examine a class of deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical…
We argue that the total observable entropy is bounded by the inverse of the cosmological constant. This holds for all space-times with a positive cosmological constant, including cosmologies dominated by ordinary matter, and recollapsing…
Our everyday reality is characterized by objective information$\unicode{x2013}$information that is selected and amplified by the environment that interacts with quantum systems. Many observers can accurately infer that information…