in the paper Circuit knitting with classical communication by Christophe Piveteau and David Sutter, the main claim is that one can reduce the cost of circuit knitting based simulation by replacing gates between two subcircuits $A$ and $B$ by a teleportation and preparing mutiple Bell pairs simulateneously (see image below).
My question is: why are two circuits considered "local" if we need to prepare a shared Bell state? The fact we prepare a Bell state means we need to be able to do a two qubit gate between them anyway, no? And from a practical standpoint in an experiment, is there any inherent advantage to this scheme?
