  A Bell test separates quantum mechanics from a classical, local realist
theory of physics. However, a Bell test cannot separate quantum physics from
all classical theories. Classical devices supplemented with non-signaling
correlations, e.g., the Popescu-Rohrlich "nonlocal box," can pass a Bell test
with probability at least as high as any quantum devices can. After all,
quantum entanglement does not allow for signaling faster than the speed of
light, so in a sense is a weaker special case of non-signaling correlations. It
could be that underneath quantum mechanics is a deeper non-signaling theory.
  We present a test to separate quantum theory from powerful non-signaling
theories. The test extends the CHSH game to involve three space-like separated
devices. Quantum devices sharing a three-qubit GHZ state can pass the test with
probability 5.1% higher than classical devices sharing arbitrary non-signaling
correlations between pairs.
  More generally, we give a test that k space-like separated quantum devices
can pass with higher probability than classical devices sharing arbitrary
(k-1)-local non-signaling correlations.
