  Vaidman described how a team of three players, each of them isolated in a
remote booth, could use a three-qubit Greenberger-Horne-Zeilinger state to
always win a game which would be impossible to always win without quantum
resources. However, Vaidman's method requires all three players to share a
common reference frame; it does not work if the adversary is allowed to
disorientate one player. Here we show how to always win the game, even if the
players do not share any reference frame. The introduced method uses a 12-qubit
state which is invariant under any transformation $R_a \otimes R_b \otimes R_c$
(where $R_a = U_a \otimes U_a \otimes U_a \otimes U_a$, where $U_j$ is a
unitary operation on a single qubit) and requires only single-qubit
measurements. A number of further applications of this 12-qubit state are
described.
