*Locality and a bound on entanglement assistance to classical communication*
A physical theory respecting locality should not allow signaling between
spacelike separated parts. However, in itself the "no-signaling"
condition does not imply that cross-correlations must fit in the
framework of quantum physics. Quantum correlations - unlike classical
ones - can violate the Bell inequality, but e.g. they do satisfy
Tsirelson's bound which in general are exceeded by non-signaling
correlations.

Many physical principles have been proposed to explain the non-existence
of "super-quantum" correlations. A notable one is "Information
Causality", which is expressed in terms of mutual information. However -
as we did in the previous article "Classical information storage in an
n-level quantum system" - instead of inequalities regarding
entropy-related quantities, here we consider the question of exact
classical simulations.

Suppose Alice receives an *X* ∈ {0,1}^{n} but can send only *m* < *n* classical bits (cbits) to Bob, who then needs to assign a value to *Z*. The "transfer matrix" (*p*(*Z=z*|*X=x*))_{{x,z}} they realize depends on their strategy and the resources they can use. In general, having a shared quantum bipartite system in some entangled state also allows them to realize transfer matrices impossible to achieve classically. However, in contrast to the generic non-signaling case, it seems (and in some cases we prove) that here the transmission of *m* cbits + the use of a quantum bipartite system - regardless of its size - can be always simulated by a transmission of 2*m* cbits. I will comment on physical interpretations and on how this could be seen as a constraint on the possible convex structure of the state-space of a system. (Work in progress; joint with P.E. Frenkel.)