The gravity dual of a density matrix

Abstract

For a state in a quantum field theory on some spacetime, we can associate a\ndensity matrix to any subset of a given spacelike slice by tracing out the\nremaining degrees of freedom. In the context of the AdS/CFT correspondence, if\nthe original state has a dual bulk spacetime with a good classical description,\nit is natural to ask how much information about the bulk spacetime is carried\nby the density matrix for such a subset of field theory degrees of freedom. In\nthis note, we provide several constraints on the largest region that can be\nfully reconstructed, and discuss specific proposals for the geometric\nconstruction of this dual region.\n