Renyi information from entropic effects in one higher dimension

Abstract

Computing entanglement entropy and its cousins is often challenging even in the simplest continuum and lattice models, partly because such entropies depend nontrivially on all geometric characteristics of the entangling region. Quantum information measures between two or more regions are even more complicated, but contain more, and universal, information. In this paper, we focus on Rényi entropy and information of the order $n=2$. For a free field theory, we show that these quantities are mapped to the change of the thermodynamic free energy by introducing boundaries subject to Dirichlet and Neumann boundary conditions in one higher dimension. This mapping allows us to exploit the powerful tools available in the context of thermal Casimir effect, specifically a multipole expansion suited for computing the Rényi information between arbitrarily-shaped regions. In particular, we compute the Rényi information between two disk-shaped regions at an arbitrary separation distance. We provide an alternative representation of the Rényi information as a sum over closed-loop polymers, which establishes a connection to purely entropic effects, and proves useful in deriving information inequalities. Finally, we discuss extensions of our results beyond free field theories.

30 pages, 12 figures. A number of new results on mutual information between regions of various shapes at arbitrary separations added

References in corpus (13)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Universal terms for the entanglement entropy in 2+1 dimensions
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Worldline algorithms for Casimir configurations
• Casimir Forces between Compact Objects: I. The Scalar Case
• Some Calculable Contributions to Entanglement Entropy
• Universal behavior of a bipartite fidelity at quantum criticality
• Casimir manipulations: The orientation dependence of fluctuation-induced forces
• Mutual Rényi information for two disjoint compound systems
• Renyi information from entropic effects in one higher dimension
• Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension
• Reversing the Critical Casimir force by shape deformation

Cited by in corpus (2)

• Formation probabilities in quantum critical chains and Casimir effect
• Renyi information from entropic effects in one higher dimension