Topic
Quantum relative entropy
About: Quantum relative entropy is a research topic. Over the lifetime, 3138 publications have been published within this topic receiving 108005 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, a systematic study of entanglement entropy in relativistic quantum field theory is carried out, where the von Neumann entropy is defined as the reduced density matrix ρA of a subsystem A of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, and the results are verified for a free massive field theory.
Abstract: We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy SA = −Tr ρAlogρA corresponding to the reduced density matrix ρA of a subsystem A. For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, we re-derive the result of Holzhey et al when A is a finite interval of length in an infinite system, and extend it to many other cases: finite systems, finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length ξ is large but finite, we show that , where is the number of boundary points of A. These results are verified for a free massive field theory, which is also used to confirm a scaling ansatz for the case of finite size off-critical systems, and for integrable lattice models, such as the Ising and XXZ models, which are solvable by corner transfer matrix methods. Finally the free field results are extended to higher dimensions, and used to motivate a scaling form for the singular part of the entanglement entropy near a quantum phase transition.
3,029 citations
TL;DR: In this paper, a renormalized entropy is defined as the difference in the entropy relative to the ground state of a quantum field theory excited by a moving mirror, and it is shown that the entropy can diverge for sharply localized states.
1,798 citations
TL;DR: In this article, the authors provide a derivation of holographic entanglement entropy for spherical entangling surfaces, which relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry.
Abstract: We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to the entanglement entropy is given by A-type trace anomaly for any CFT, without reference to holography.
1,601 citations
TL;DR: This work associates to any quantum field propagating in the background metric of a black hole an effective density matrix whose statistical entropy can be interpreted as a contribution to the total entropy of the black hole.
Abstract: We associate to any quantum field propagating in the background metric of a black hole an effective density matrix whose statistical entropy can be interpreted as a contribution to the total entropy of the black hole. By evaluating this contribution in a simplified case, we show that in general it can be expected to be finite and proportional to the area of the black hole. As a by-product of our calculation we obtain a general expression for the entropy of any real Gaussian density matrix.
1,518 citations
TL;DR: In this article, the authors considered the problem of computing the trace of a density matrix in the full quantum gravity theory, in the classical approximation, and showed that the entropy of this density matrix is given by the area of a minimal surface.
Abstract: We consider classical Euclidean gravity solutions with a boundary. The bound- ary contains a non-contractible circle. These solutions can be interpreted as computing the trace of a density matrix in the full quantum gravity theory, in the classical approximation. When the circle is contractible in the bulk, we argue that the entropy of this density matrix is given by the area of a minimal surface. This is a generalization of the usual black hole entropy formula to euclidean solutions without a Killing vector. A particular example of this set up appears in the computation of the entanglement entropy of a subregion of a field theory with a gravity dual. In this context, the minimal area prescription was proposed by Ryu and Takayanagi. Our arguments explain their conjecture.
1,332 citations