  We demonstrate how to universally simulate ensemble statistics of projective
local measurements on any $n$-qubit state shared among $n$ observers with
classical communication and shared randomness. Our technique originates from
protocols designed to simulate quantum non-locality [in Horizons of the Mind,
Springer, Cham (2014)] and classical simulation of quantum circuits [Phys. Rev.
Lett. 115, 070501 (2015)]. The protocol preserves three crucial aspects of the
simulated quantum scenario in contrast to other approaches: no involvement of
additional parties, none of the observers knows the global state of the system,
and local measurement settings remain undisclosed.
