## 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 $\mathrm{\U0001d5a1\U0001d5b5}$ 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 $\mathrm{\U0001d5a1\U0001d5b5}$ are developed as part of this analysis, which is published in [28]