The R{é}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{é}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital importance. Another important quantity is R{é}nyi relative entropy on which R{é}nyi generalization of the conditional entropy, and mutual information are defined based. Thus, finding lower bound for R{é}nyi relative entropy is our goal in this paper. We use matrix inequalities to prove new bounds on the entropy of type $β$ , R{é}nyi entropy.The R{é}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{é}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital importance. Another important quantity is R{é}nyi relative entropy on which R{é}nyi generalization of the conditional entropy, and mutual information are defined based. Thus, finding lower bound for R{é}nyi relative entropy is our goal in this paper. We use matrix inequalities to prove new bounds on the entropy of type $β$, R{é}nyi entropy.

arXiv:1608.03362Aug 11, 20160 citations

Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo

David J. Luitz, Xavier Plat, Nicolas Laflorencie +1 more

We present a method for improving measurements of the entanglement R\'enyi entropies in quantum Monte Carlo simulations by relating them with measurements of participation R\'enyi entropies. Exploiting the capability of building improved estimators for the latter makes it possible to obtain very good estimates for entanglement R\'enyi entropies. When considering a full system instead of a bipartition, the method can be further ameliorated, providing access to the thermodynamic R\'enyi entropies with high accuracy. We also explore a recently proposed method for the reconstruction of the entanglement spectrum from entanglement R\'enyi entropies and finally show how potential entanglement Hamiltonians may be tested for their validity using a comparison with thermal R\'enyi entropies.We present a method for improving measurements of the entanglement R\'enyi entropies in quantum Monte Carlo simulations by relating them with measurements of participation R\'enyi entropies. Exploiting the capability of building improved estimators for the latter makes it possible to obtain very good estimates for entanglement R\'enyi entropies. When considering a full system instead of a bipartition, the method can be further ameliorated, providing access to the thermodynamic R\'enyi entropies with high accuracy. We also explore a recently proposed method for the reconstruction of the entanglement spectrum from entanglement R\'enyi entropies and finally show how potential entanglement Hamiltonians may be tested for their validity using a comparison with thermal R\'enyi entropies.

arXiv:1405.7391Physical Review BSep 3, 201459 citations

Rényi Entropy and Complexity

Ágnes Nagy, E. Romera

Springer eBooksJan 1, 20114 citations

Logarithmic singularities of Renyi entropy as a sign of chaos?

Norihiro Iizuka, Mitsuhiro Nishida

A bstract We propose that the logarithmic singularities of the Renyi entropy of local-operator-excited states for replica index n can be a sign of quantum chaos. As concrete examples, we analyze the logarithmic singularities of the Renyi entropy in various two-dimensional conformal field theories. We show that there are always logarithmic singularities of the Renyi entropy in holographic CFTs, but no such singularities in free and rational CFTs. These singularities of the Renyi entropy are also related to the logarithmic time growth of the Renyi entropy at late times.A bstract We propose that the logarithmic singularities of the Renyi entropy of local-operator-excited states for replica index n can be a sign of quantum chaos. As concrete examples, we analyze the logarithmic singularities of the Renyi entropy in various two-dimensional conformal field theories. We show that there are always logarithmic singularities of the Renyi entropy in holographic CFTs, but no such singularities in free and rational CFTs. These singularities of the Renyi entropy are also related to the logarithmic time growth of the Renyi entropy at late times.

arXiv:2404.04805Journal of High Energy PhysicsOct 4, 20241 citation

Conditional Rényi Entropy

Marco Tomamichel

SpringerBriefs in mathematical physicsOct 8, 20154 citations

β

, R{é}nyi entropy.