Final Report Summary - QMULT (Multipartite Quantum Information Theory)
The project has developed tools and ideas in order to bring quantum communication theory from a point to point communication theory to a truly multiparty communication theory. The project had a dual focus. On the one hand focusing on multiparticle entanglement through its connection to tensor research and, on the other hand, focusing on structural aspects of multiparty coding theory. With respect to the first focal point - entanglement - the project has opened a new line of research bringing the tools of entanglement research and tensor research together. The project has resulted in a series of papers on the understanding of the asymptotic conversion among higher order tensors, motivated by the problem of understanding the complexity of matrix multiplication. Using quantum information tools and intuition we made, in this context, significant headway on a problem of Strassen from 1986 which asks for the constructions of lower bounds to tensor transformations (or additive entanglement monotones). With respect to the second focal point, we - for the first time - considered the question of whether there is a difference in the distribution of entanglement or secret key when considering a network of nodes, rather than a point-to-point network. Surprisingly, we were able to present a significant difference: there are quantum correlations that are sufficiently strong so that secret bits can be extracted, but not strong enough in order to distribute them among two distant nodes in a network.