Causal Boxes: Quantum Information-Processing Systems Closed under Composition

Abstract

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.

44+24 pages, 16 figures. v3: minor edits based on referee comments, matches published version up to layout. v2: definition of causality weakened, new references

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Cited by in corpus (29)

• Security in Quantum Cryptography
• Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories
• Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders
• Resource theories of multi-time processes: A window into quantum non-Markovianity
• Genuine Multipartite Entanglement in Time
• Causal structure in the presence of sectorial constraints, with application to the quantum switch
• The entropic approach to causal correlations
• Composable security in relativistic quantum cryptography
• Relaxation of Multitime Statistics in Quantum Systems
• Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
• A general framework for cyclic and fine-tuned causal models and their compatibility with space-time
• Causal and compositional structure of unitary transformations
• Equilibration of Multitime Quantum Processes in Finite Time Intervals
• Quantum steering beyond instrumental causal networks
• Security of differential phase shift QKD from relativistic principles
• Fundamental limits for realising quantum processes in spacetime
• Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise
• Operational Markovianization in Randomized Benchmarking
• Categorical composable cryptography
• Addressable quantum gates
• The Multi-round Process Matrix
• The Möbius game and other Bell tests for relativity
• The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
• Mapping indefinite causal order processes to composable quantum protocols in a spacetime
• Operational interpretation of the vacuum and process matrices for identical particles
• On the composable security of weak coin flipping
• Incorporating device characterization into security proofs
• Flow of dynamical causal structures with an application to correlations
• Causal influence versus signalling for interacting quantum channels