Spatially Delocalized Operators and Faster-than-light Signaling

Sammanfattning

This paper explores the relationship between locality and causality for delocalized quantum operations within the framework of non-relativistic quantum mechanics. By defining and contrasting classes of local, shared-randomness localizable, shared-entanglement localizable, and causal bipartite superoperators, we establish a strict hierarchy of possible operations. Within the class of complete orthogonal measurement superoperators (COMS), we derive precise causality conditions and employ communication complexity arguments to determine nonlocalizability. Extending the analysis to Haar-random COMS, we compute the expected signaling in finite dimensions and show numerically that it vanishes in the large-dimension limit, offering a quantitative interpretation of macroscopic causality as an emergent phenomenon. These results clarify the distinctions between mathematical implementability and physical admissibility, and provide a framework for further exploration of nonlocal and causal structures in quantum theory.