def test_complete_depolarizing(self):
"""Maps every density matrix to the maximally-mixed state."""
test_input_mat = np.array([[1 / 2, 0, 0, 1 / 2], [0, 0, 0, 0],
[0, 0, 0, 0], [1 / 2, 0, 0, 1 / 2]])
expected_res = (1 / 4 * np.array([[1 / 2, 0, 0, 1 / 2], [0, 0, 0, 0],
[0, 0, 0, 0], [1 / 2, 0, 0, 1 / 2]]))
res = apply_map(test_input_mat, depolarizing(4))
bool_mat = np.isclose(expected_res, res)
self.assertEqual(np.all(bool_mat), True)
def test_partially_depolarizing(self):
"""The partially depolarizing channel for `p = 0.5`."""
test_input_mat = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12],
[13, 14, 15, 16]])
expected_res = np.array([
[17.125, 0.25, 0.375, 0.5],
[0.625, 17.75, 0.875, 1],
[1.125, 1.25, 18.375, 1.5],
[1.625, 1.75, 1.875, 19],
])
res = apply_map(test_input_mat, depolarizing(4, 0.5))
bool_mat = np.isclose(expected_res, res)
self.assertEqual(np.all(bool_mat), True)
def test_partial_map_dim_list(self):
"""
Perform the partial map using the depolarizing channel as the Choi
matrix on first system when the dimension is specified as list.
"""
rho = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12],
[13, 14, 15, 16]])
res = partial_map(rho, depolarizing(2), 2, [2, 2])
expected_res = np.array([
[3.5, 0.0, 5.5, 0.0],
[0.0, 3.5, 0.0, 5.5],
[11.5, 0.0, 13.5, 0.0],
[0.0, 11.5, 0.0, 13.5],
])
bool_mat = np.isclose(expected_res, res)
self.assertEqual(np.all(bool_mat), True)
def test_partial_map_depolarizing_second_system(self):
"""
Perform the partial map using the depolarizing channel as the Choi
matrix on second system.
"""
rho = np.array([
[
0.3101,
-0.0220 - 0.0219 * 1j,
-0.0671 - 0.0030 * 1j,
-0.0170 - 0.0694 * 1j,
],
[
-0.0220 + 0.0219 * 1j,
0.1008,
-0.0775 + 0.0492 * 1j,
-0.0613 + 0.0529 * 1j,
],
[
-0.0671 + 0.0030 * 1j,
-0.0775 - 0.0492 * 1j,
0.1361,
0.0602 + 0.0062 * 1j,
],
[
-0.0170 + 0.0694 * 1j,
-0.0613 - 0.0529 * 1j,
0.0602 - 0.0062 * 1j,
0.4530,
],
])
res = partial_map(rho, depolarizing(2), 1)
expected_res = np.array([
[0.2231 + 0.0j, 0.0191 - 0.00785j, 0.0 + 0.0j, 0.0 + 0.0j],
[0.0191 + 0.00785j, 0.2769 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j],
[0.0 + 0.0j, 0.0 + 0.0j, 0.2231 + 0.0j, 0.0191 - 0.00785j],
[0.0 + 0.0j, 0.0 + 0.0j, 0.0191 + 0.00785j, 0.2769 + 0.0j],
])
bool_mat = np.isclose(expected_res, res)
self.assertEqual(np.all(bool_mat), True)
def test_is_positive_choi_true(self):
"""
Verify that the Choi matrix of the depolarizing map is positive.
"""
self.assertEqual(is_positive(depolarizing(4)), True)
def test_invalid_dim(self):
"""Invalid dimension for partial map."""
with self.assertRaises(ValueError):
rho = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [12, 11, 10, 9]])
partial_map(rho, depolarizing(3), 1, [2, 2])
def test_non_square_matrix_2(self):
"""Matrix must be square."""
with self.assertRaises(ValueError):
rho = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [12, 11, 10, 9]])
partial_map(rho, depolarizing(3), 2)
def test_non_square_matrix(self):
"""Matrix must be square."""
with self.assertRaises(ValueError):
rho = np.array([[1, 1, 1, 1], [5, 6, 7, 8], [3, 3, 3, 3]])
partial_map(rho, depolarizing(3))