Related papers: Mutual information superadditivity and unitarity b…
We argue in a quantitative way that the unitarity principle of quantum field theory together with the quantum information bound on correlation functions are in tension with a space which is made out of disconnected patches at microscopic…
We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in $1+1$ space-time dimensions.…
Active learning for continuous regression has lacked an acquisition function that targets epistemic uncertainty when the predictive distribution is multimodal: variance misses modal disagreement, and information-theoretic targets like BALD…
We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions, and are thus the most classical ones among all possible…
We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…
We derive the closed-form expression of the maximum mutual information - the maximum value of $I(X;Z)$ obtainable via training - for a broad family of neural network architectures. The quantity is essential to several branches of machine…
We analyze geometric terms and scaling properties of the Shannon mutual information in the continuum. This is done for a free massless scalar field theory in $d$-dimensions, in a coherent state reduced with respect to a general…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
While the quantum mutual information is a fundamental measure of quantum information, it is only defined for spacelike-separated quantum systems. Such a limitation is not present in the theory of classical information, where the mutual…
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 derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
We characterize the growth of the Sibson and Arimoto mutual informations and $\alpha$-maximal leakage, of any order that is at least unity, between a random variable and a growing set of noisy, conditionally independent and…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
The work is devoted to study of quantum mutual information and coherent information -- the two important characteristics of quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are…
A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly $(c/3)\ln \ell$ for an interval of length $\ell$ in an infinite system, where $c$…
We consider universal methods for obtaining (uniform) continuity bounds for characteristics of multipartite quantum systems. We pay a special attention to infinite-dimensional multipartite quantum systems under the energy constraints. By…
An unsupervised learning procedure based on maximizing the mutual information between the outputs of two networks receiving different but statistically dependent inputs is analyzed (Becker and Hinton, Nature, 355, 92, 161). For a generic…
Information shared between parties quantifies their correlation. The encoding of correlations across space and time characterises the structure, history, and interactions of systems. One of the most fundamental properties that emerges from…
Squashed entanglement and its universal upper bound, the quantum conditional mutual information, are faithful measures of bipartite quantum correlations defined in terms of multipartitions. As such, they are sensitive to the fine-grain…
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…