Section: New Results

A logical basis for quantum evolution and entanglement

Participant : Lutz Straßburger.

In discrete quantum causal dynamics, quantum systems are viewed as discrete structures, namely directed acyclic graphs. In such a graph, events are considered as vertices and edges depict propagation between events. Evolution is described as happening between a special family of space-like slices, which were referred to as locative slices in  [41] . Such slices are not so large as to result in acausal influences, but large enough to capture nonlocal correlations. It was an open problem whether such slices can be captured by a deductive system, such that proof search corresponds to quantum evolution. In a joint work with Blute, Guglielmi, Ivanov, and Panangaden, Straßburger has shown that the logic $\mathrm{𝖡𝖵}$ with its mix of commutative and noncommutative connectives, is precisely the right logic for such analysis. More precisely, it was shown that the commutative tensor encodes (possible) entanglement, and the noncommutative seq encodes causal precedence. With this interpretation, the locative slices are precisely the derivable strings of formulas. Several new technical results about $\mathrm{𝖡𝖵}$ are developed as part of this analysis, which is published in [28]