Generalised tensors and traces

Tensors and traceouts are generalized so that systems can be partitioned according to almost arbitrary logical predicates. One might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signaling causality, locality, and localizability that are standard in quantum theory be jeopardized as the partitioning of systems becomes both logical and dynamical. Such interrelations in fact carry through. These generalized operators may naturally lead to generalized and thereby more robust notions of entanglement.