Causal Density Matrices
arXiv:1703.05328 · doi:10.1103/PhysRevD.95.126012
Abstract
We define a new construct in quantum field theory - the causal density matrix - obtained from the singularity structure of correlators of local operators. This object provides a necessary and sufficient condition for a quantum field theory state to have a holographic semiclassical dual causal geometry. By exploiting the causal density matrix, we find that these dual causal geometries quite generally (even away from AdS/CFT) exhibit features of quantum error correction. Within AdS/CFT, we argue that the "reduced" causal density matrix is the natural dual to the causal wedge. Our formalism is very well-suited to generalizations of holography beyond AdS/CFT or even gravity/QFT.
34+4 pages, 10 figures. v2: minor edits, references added. v3: minor typos corrected
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