相关论文: A R\'enyi entropy perspective on topological order…

Entanglement entropy is a fundamental measure of quantum entanglement for pure states, but for large-scale many-body systems, R\'{e}nyi entanglement entropy is much more computationally accessible. For mixed states, logarithmic negativity…

Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…

Phase-space versions of quantum mechanics -- from Wigner's original distribution to modern discrete-qudit constructions -- represent some states with negative quasi-probabilities. Conventional Shannon and R\'enyi entropies become…

The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…

Since their introduction in the early sixties, the R\'enyi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between…

We propose and experimentally measure an entropy that quantifies the volume of correlations among qubits. The experiment is carried out on a nearly isolated quantum system composed of a central spin coupled and initially uncorrelated with…

An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…

In this paper, we study the holographic R\'enyi entropy of a large interval on a circle at high temperature for the two-dimensional conformal field theory (CFT) dual to pure AdS$_3$ gravity. In the field theory, the R\'enyi entropy is…

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

Topological quantum many-body systems, such as Hall insulators, are characterized by a hidden order encoded in the entanglement between their constituents. Entanglement entropy, an experimentally accessible single number that globally…

We study the statistical physics of the classical Ising model in the so-called $\alpha$-R\'enyi ensemble, a finite-temperature thermal state approximation that minimizes a modified free energy based on the $\alpha$-R\'enyi entropy. We begin…

We present a new method to compute R\'enyi entropies in one-dimensional critical systems. The null-vector conditions on the twist fields in the cyclic orbifold allow us to derive a differential equation for their correlation functions. The…

We introduce several new quantum algorithms for estimating homological invariants, specifically Betti numbers and persistent Betti numbers, of a simplicial complex given via a structured classical input. At the core of our algorithm lies…

We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…

In a D=2+1 quantum critical system, the entanglement entropy across a boundary with a corner contains a subleading logarithmic scaling term with a universal coefficient. It has been conjectured that this coefficient is, to leading order,…

We study both entanglement and the R\'enyi entropies for the 2 dimensional massless Dirac fermions in the presence of topological Wilson loops, which are qualitatively different from those with a chemical potential and a current source. In…

Using a Corner Transfer Matrix approach, we compute the bipartite entanglement R\'enyi entropy in the off-critical perturbations of non-unitary conformal minimal models realised by lattice spin chains Hamiltonians related to the Forrester…

Conservation laws and the associated hydrodynamic modes have important consequences on the growth of higher R\'enyi entropies in isolated quantum systems. It has been shown in various random unitary circuits and Hamiltonian systems that the…

We study the R\'enyi mutual information $\tilde{I}_n$ of the ground state of different critical quantum chains. The R\'enyi mutual information definition that we use is based on the well established concept of the R\'enyi divergence. We…

We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of…