Entanglement measures and the quantum-to-classical mapping

A quantum model can be mapped to a classical model in one higher dimension. Here we introduce a finite-temperature correlation measure based on a reduced density matrix rho((A) over bar) obtained by cutting the classical system along the imaginary time (inverse temperature) axis. We show that the von-Neumann entropy (S) over bar (ent) of (rho) over bar ((A) over bar) shares many properties with the mutual information, yet is based on a simpler geometry and is thus easier to calculate. For one-dimensional quantum systems in the thermodynamic limit we proof that (S) over bar (ent) is non-extensive for all temperatures T. For the integrable transverse Ising and XXZ models we demonstrate that the entanglement spectra of (rho) over bar ((A) over bar) in the limit T -> 0 are described by free-fermion Hamiltonians and reduce to those of the regular reduced density matrix rho(A)-obtained by a spatial instead of an imaginary-time cut-up to degeneracies.