Bicategorical Semantics for Nondeterministic Computation
This work provides a foundational framework for understanding classical information protocols, potentially bridging classical and quantum domains, but it is incremental as it builds on existing bicategorical methods.
The paper tackles the problem of modeling interactions between public and private information in classical information theory by introducing a bicategorical syntax, which reveals that encrypted communication and secret sharing protocols share an identical abstract form with quantum teleportation and dense coding, suggesting a deep connection between classical and quantum information processing.
We outline a bicategorical syntax for the interaction between public and private information in classical information theory. We use this to give high-level graphical definitions of encrypted communication and secret sharing protocols, including a characterization of their security properties. Remarkably, this makes it clear that the protocols have an identical abstract form to the quantum teleportation and dense coding procedures, yielding evidence of a deep connection between classical and quantum information processing. We also formulate public-key cryptography using our scheme. Specific implementations of these protocols as nondeterministic classical procedures are recovered by applying our formalism in a symmetric monoidal bicategory of matrices of relations.