Complex information-processing systems, for example quantum circuits,
cryptographic protocols, or multi-player games, are naturally described as
networks composed of more basic information-processing systems. A modular
analysis of such systems requires a mathematical model of systems that is
closed under composition, i.e., a network of these objects is again an object
of the same type. We propose such a model and call the corresponding systems
causal boxes.
Causal boxes capture superpositions of causal structures, e.g., messages sent
by a causal box A can be in a superposition of different orders or in a
superposition of being sent to box B and box C. Furthermore, causal boxes can
model systems whose behavior depends on time. By instantiating the Abstract
Cryptography framework with causal boxes, we obtain the first composable
security framework that can handle arbitrary quantum protocols and relativistic
protocols.Comment: 44+24 pages, 16 figures. v3: minor edits based on referee comments,
matches published version up to layout. v2: definition of causality weakened,
new reference
