Related papers: Min- and Max-Entropy in Infinite Dimensions
Recently, Anshu et al. introduced "partially" smoothed information measures and used them to derive tighter bounds for several information-processing tasks, including quantum state merging and privacy amplification against quantum…
We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of…
We derive a lower bound on the smallest output entropy that can be achieved via vector quantization of a $d$-dimensional source with given expected $r$th-power distortion. Specialized to the one-dimensional case, and in the limit of…
The maximum entropy of a quantized surface is demonstrated to be proportional to the surface area in the classical limit. The result is valid in loop quantum gravity, and in a somewhat more general class of approaches to surface…
A natural measure for the amount of quantum information that a physical system E holds about another system A = A_1,...,A_n is given by the min-entropy Hmin(A|E). Specifically, the min-entropy measures the amount of entanglement between E…
The von Neumann entropy of an $n$-partite system $A_1^n$ given a system $B$ can be written as the sum of the von Neumann entropies of the individual subsystems $A_k$ given $A_1^{k-1}$ and $B$. While it is known that such a chain rule does…
Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is…
Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…
We study the existence of Riemannian metrics with zero topological entropy on a closed manifold M with infinite fundamental group. We show that such a metric does not exist if there is a finite simply connected CW complex which maps to M in…
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…
A maximum entropy-based framework is presented for the synthesis of projections from multiple Earth climate models. This identifies the most representative (most probable) model from a set of climate models -- as defined by specified…
Bipartite entanglement entropy is one of the most useful characterizations of universal properties in a many-body quantum system. Far from equilibrium, there exist two highly effective theories describing its dynamics -- the quasiparticle…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
Subshifts are sets of colorings of $\mathbb{Z}^d$ defined by families of forbidden patterns. In a given subshift, the extender set of a finite pattern is the set of all its admissible completions. Since soficity of $\mathbb{Z}$ subshifts is…
We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics and system sizes. Within the theory, the finite-entanglement scaling introduced recently is generalized to the dynamics…
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 continuous time, the laws of martingales tend to be singular to each other. Notably, N. Gantert introduced the concept of specific relative entropy between real-valued continuous martingales, defined as a scaling limit of…
The narrow and subtle difference between the Hilbert spaces of operators corresponding to the purely quantum mechanical momentum and the generalized momentum that includes minimal length effects is polished. Additionally, the existence of…
Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic…
The pervasive presence spatial and size structure in biological populations challenges fundamental assumptions at the heart of continuum models of population dynamics based on mean densities (local or global) only. Individual-based models…