Communication Protocols and QECCs from the Perspective of TQFT, Part I: Constructing LOCC Protocols and QECCs from TQFTs

Topological quantum field theories (TQFTs) provide a general,minimal-assumption language for describing quantum-state preparation andmeasurement. They therefore provide a general language in which to expressmulti-agent communication protocols, e.g. local operations, classicalcommunication (LOCC) protocols. Here we construct LOCC protocols using TQFT,and show that LOCC protocols generically induce quantum error-correcting codes(QECCs). Using multi-observer scenarios described by quantum Darwinism andBell/EPR experiments as examples, we show how these LOCC-induced QECCseffectively convert entanglement into classical redundancy. In the accompanyingPart II, we show that such QECCs can be regarded as implementing, or inducingthe emergence of, spacetimes on the boundaries between interacting systems. Weinvestigate this connection between inter-agent communication and spacetimeusing BF and Chern-Simons theories, and then using topological M-theory.