def test_invalid_dim(self):
"""Tests for invalid dim."""
rho = np.array([[1 / 2, 0, 0, 1 / 2], [0, 0, 0, 0], [0, 0, 0, 0],
[1 / 2, 0, 0, 1 / 2]])
sigma = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
with self.assertRaises(ValueError):
fidelity(rho, sigma)
def test_fidelity_non_identical_states_2(self):
"""Test the fidelity between two non-identical states."""
e_0, e_1 = ket(2, 0), ket(2, 1)
rho = 3 / 4 * e_0 * e_0.conj().T + 1 / 4 * e_1 * e_1.conj().T
sigma = 1 / 8 * e_0 * e_0.conj().T + 7 / 8 * e_1 * e_1.conj().T
self.assertEqual(np.isclose(fidelity(rho, sigma), 0.774, rtol=1e-03),
True)
def test_fidelity_default(self):
"""Test fidelity default arguments."""
rho = np.array([[1 / 2, 0, 0, 1 / 2], [0, 0, 0, 0], [0, 0, 0, 0],
[1 / 2, 0, 0, 1 / 2]])
sigma = rho
res = fidelity(rho, sigma)
self.assertEqual(np.isclose(res, 1), True)
def test_fidelity_cvx(self):
"""Test fidelity for cvx objects."""
rho = cvxpy.bmat([[1 / 2, 0, 0, 1 / 2], [0, 0, 0, 0], [0, 0, 0, 0],
[1 / 2, 0, 0, 1 / 2]])
sigma = rho
res = fidelity(rho, sigma)
self.assertEqual(np.isclose(res, 1), True)
def test_sub_fidelity_lower_bound_2(self):
"""Test sub_fidelity is lower bound on fidelity for rho and pi."""
e_0, e_1 = ket(2, 0), ket(2, 1)
rho = 3 / 4 * e_0 * e_0.conj().T + 1 / 4 * e_1 * e_1.conj().T
sigma = 1 / 8 * e_0 * e_0.conj().T + 7 / 8 * e_1 * e_1.conj().T
res = sub_fidelity(rho, sigma)
self.assertLessEqual(res, fidelity(rho, sigma))