Communication protocols and quantum error-correcting codes from the perspective of topological quantum field theory

Abstract

Topological quantum field theories (TQFTs) provide a general, minimal-assumption language for describing quantum-state preparation and measurement. They therefore provide a general language in which to express multi-agent communication protocols, e.g. local operations, classical communication (LOCC) protocols. Here we construct LOCC protocols using TQFT, and show that LOCC protocols induce quantum error-correcting codes (QECCs) on the agent-environment boundary. Such QECCs can be regarded as implementing, or inducing the emergence of, spacetimes on such boundaries. We investigate this connection between inter-agent communication and spacetime using BF and Chern-Simons theories, and then using topological M-theory.Comment: 52 page