Discrete Quantum Causal Dynamics

We give a mathematical framework to describe the evolution of open quantum systems subject to finitely many interactions with classical apparatuses and with each other. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently, but may also interact. This evolution, driven both by unitary operators and measurements, is coded in a mathematical structure in such a way that the crucial properties of causality, covariance, and entanglement are faithfully represented. The key to this scheme is the use of a special family of spacelike slices—we call them locative—that are not so large as to result in acausal influences but large enough to capture nonlocal correlations.