def test_qcb_for_mixed_states():
# both states are real so no need to conjugate
theta = np.pi / 2
G = np.array([[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)]])
r = 0.9
lam_p = r
lam_m = 1 - lam_p
rho = np.diag([lam_p, lam_m])
rho_theta = np.matmul(np.matmul(G, rho), G.transpose())
qcb, s = dm.quantum_chernoff_bound(rho, rho_theta)
assert np.allclose(
dm.quantum_chernoff_bound(rho, rho_theta)[0], 0.59999999999)
def test_qcb_for_pure_states():
# both states are real so no need to conjugate
zero = np.array([[1], [0]])
rho = np.matmul(zero, zero.transpose())
theta = np.pi / 2
psi_theta = np.array([[np.cos(theta / 2)], [np.sin(theta / 2)]])
sigma = np.matmul(psi_theta, psi_theta.transpose())
assert np.allclose(dm.quantum_chernoff_bound(rho, sigma)[0], 0.5000000000)