Metric Fisher and entropy entanglement

Alexander Rudol'fovich Its, V. E. Korepin

Hristo Dimov, Stefan Mladenov, Radoslav C. Rashkov +1 more

We derive the extended renormalized entanglement entropy and the Fisher information metric in the case of closed bosonic strings in a homogeneous plane wave background. Our investigations are conducted within the framework of thermo field dynamics. The formalism is also illustrated in the example of some particular models in condensed matter physics and the nonequilibrium case for a system with dissipations.

Dominik Janzing

Marin Drinov Academic Publishing House, T. Vetsov, Radoslav C. Rashkov

We derive the extended entanglement entropy and the Fisher information metric in the case of quantum models, described by time-independent diagonal quadratic Hamiltonians. Our research is conducted within the framework of Thermo field dynamics. We also study the properties of the Fisher metric invariants to identify the phase structure of the quasi-particle systems in equilibrium.

Raimond Abt, Johanna Erdmenger B

Abstract The modular Hamiltonian of reduced states, given essentially by the logarithm of the reduced density matrix, plays an important role within the AdS/CFT correspondence in view of its relation to quantum information. In particular, it is an essential ingredient for quantum information measures of distances between states, such as the relative entropy and the Fisher information metric. However, the modular Hamiltonian is known explicitly only for a few examples. For a family of states ρ λ that is parametrized by a scalar λ, the first order contribution in $$ \overset{\sim }{\lambda } = \lambda -{\lambda}_0 $$ λ ∼ = λ − λ 0 of the modular Hamiltonian to the relative entropy between ρλ and a reference state ρλ 0 is completely determined by the entanglement entropy, via the first law of entanglement. For several examples, e.g. for ball-shaped regions in the ground state of CFTs, higher order contributions are known to vanish. In these cases the modular Hamiltonian contributes to the Fisher information metric in a trivial way. We investigate under which conditions the modular Hamiltonian provides a non-trivial contribution to the Fisher information metric, i.e. when the contribution of the modular Hamiltonian to the relative entropy is of higher order in $$ \overset{\sim }{\lambda } $$ λ ∼ . We consider one-parameter families of reduced states on two entangling regions that form an entanglement plateau, i.e. the entanglement entropies of the two regions saturate the Araki-Lieb inequality. We show that in general, at least one of the relative entropies of the two entangling regions is expected to involve $$ \overset{\sim }{\lambda } $$ λ ∼ contributions of higher order from the modular Hamiltonian. Furthermore, we consider the implications of this observation for prominent AdS/CFT examples that form entanglement plateaux in the large N limit.