def test_ffl_game_classical_value_rep_2(self):
"""Classical value for the FFL game for 2 reps."""
prob_mat, pred_mat = self.ffl_nonlocal_game()
ffl = NonlocalGame(prob_mat, pred_mat, 2)
res = ffl.classical_value()
expected_res = 2 / 3
self.assertEqual(np.isclose(res, expected_res), True)
def test_ffl_game_quantum_value_lower_bound_value_rep_2(self):
"""Lower bound on quantum value for the FFL game for 2 reps."""
prob_mat, pred_mat = self.ffl_nonlocal_game()
ffl = NonlocalGame(prob_mat, pred_mat, 2)
res = ffl.quantum_value_lower_bound()
expected_res = 2 / 3
self.assertLessEqual(np.isclose(res, expected_res), True)
def test_chsh_game_classical_value(self):
"""Classical value for the CHSH game."""
prob_mat, pred_mat = self.chsh_nonlocal_game()
chsh = NonlocalGame(prob_mat, pred_mat)
res = chsh.classical_value()
expected_res = 3 / 4
self.assertEqual(np.isclose(res, expected_res), True)
def test_chsh_game_nonsignaling_value_rep_2(self):
"""Non-signaling value for the CHSH game for 2 reps."""
prob_mat, pred_mat = self.chsh_nonlocal_game()
chsh = NonlocalGame(prob_mat, pred_mat, 2)
res = chsh.nonsignaling_value()
expected_res = 1
self.assertEqual(np.isclose(res, expected_res, atol=0.5), True)
def test_ffl_game_nonsignaling_value_rep_2(self):
"""Non-signaling value for the FFL game for 2 reps."""
prob_mat, pred_mat = self.ffl_nonlocal_game()
ffl = NonlocalGame(prob_mat, pred_mat, 2)
res = ffl.nonsignaling_value()
expected_res = 2 / 3
self.assertEqual(np.isclose(res, expected_res, atol=0.5), True)
def test_chsh_lower_bound(self):
"""Calculate the lower bound on the quantum value for the CHSH game."""
prob_mat, pred_mat = self.chsh_nonlocal_game()
chsh = NonlocalGame(prob_mat, pred_mat)
res = chsh.quantum_value_lower_bound()
# It may be possible for the lower bound to not be equal to the correct
# quantum value (as it may get stuck in a local minimum), but it should
# never be possible for the lower bound to attain a value higher than
# the true quantum value.
self.assertLessEqual(np.isclose(res, np.cos(np.pi / 8) ** 2, rtol=1e-02), True)
def test_chsh_game_classical_value_rep_2(self):
r"""
Classical value for the CHSH game for 2 reps.
Note that for classical strategies, it is known that parallel repetition
does *not* hold for the CHSH game, that is:
w_c(CHSH \land CHSH) = 10/16 > 9/16 = w_c(CHSH) w_c(CHSH).
"""
prob_mat, pred_mat = self.chsh_nonlocal_game()
chsh = NonlocalGame(prob_mat, pred_mat, 2)
res = chsh.classical_value()
expected_res = 10 / 16
self.assertEqual(np.isclose(res, expected_res), True)