Causal Density Matrices

Understand

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.