def test_schmidt_rank_bell_state():
"""
Computing the Schmidt rank of the entangled Bell state should yield a
value greater than 1.
"""
rho = bell(0).conj().T * bell(0)
np.testing.assert_equal(schmidt_rank(rho) > 1, True)
def test_schmidt_rank_singlet_state():
"""
Computing the Schmidt rank of the entangled singlet state should yield
a value greater than 1.
"""
e_0, e_1 = basis(2, 0), basis(2, 1)
rho = 1 / np.sqrt(2) * (np.kron(e_0, e_1) - np.kron(e_1, e_0))
np.testing.assert_equal(schmidt_rank(rho) > 1, True)
def test_schmidt_rank_entangled_state():
"""Computing Schmidt rank of entangled state should be > 1."""
e_0, e_1 = basis(2, 0), basis(2, 1)
phi = (
(1 + np.sqrt(6)) / (2 * np.sqrt(6)) * np.kron(e_0, e_0)
+ (1 - np.sqrt(6)) / (2 * np.sqrt(6)) * np.kron(e_0, e_1)
+ (np.sqrt(2) - np.sqrt(3)) / (2 * np.sqrt(6)) * np.kron(e_1, e_0)
+ (np.sqrt(2) + np.sqrt(3)) / (2 * np.sqrt(6)) * np.kron(e_1, e_1)
)
np.testing.assert_equal(schmidt_rank(phi) == 2, True)
def test_schmidt_rank_separable_state():
"""
Computing the Schmidt rank of a separable state should yield a value
equal to 1.
"""
e_0, e_1 = basis(2, 0), basis(2, 1)
e_00 = np.kron(e_0, e_0)
e_01 = np.kron(e_0, e_1)
e_10 = np.kron(e_1, e_0)
e_11 = np.kron(e_1, e_1)
rho = 1 / 2 * (e_00 - e_01 - e_10 + e_11)
np.testing.assert_equal(schmidt_rank(rho) == 1, True)
def test_schmidt_rank_bell_density_matrices():
"""Computing Schmidt rank of Bell density matrices should be 4."""
np.testing.assert_equal(schmidt_rank(bell(0) * bell(0).conj().T) == 4, True)
np.testing.assert_equal(schmidt_rank(bell(1) * bell(1).conj().T) == 4, True)
np.testing.assert_equal(schmidt_rank(bell(2) * bell(2).conj().T) == 4, True)
np.testing.assert_equal(schmidt_rank(bell(3) * bell(3).conj().T) == 4, True)
np.testing.assert_equal(schmidt_rank(bell(0) * bell(0).conj().T, [2, 2]) == 4, True)
np.testing.assert_equal(schmidt_rank(bell(0) * bell(0).conj().T, 2) == 4, True)
def test_schmidt_rank_bell_state():
"""
Computing the Schmidt rank of the entangled Bell state should yield a
value greater than 1.
"""
np.testing.assert_equal(np.isclose(schmidt_rank(bell(0)), 2), True)
def test_schmidt_rank_bell_state_list():
"""
Computing the Schmidt rank of Bell state with list as argument for dims.
"""
np.testing.assert_equal(np.isclose(schmidt_rank(bell(0), [2, 2]), 2), True)
def test_schmidt_rank_bell_state_dim_1():
"""
Computing the Schmidt rank of Bell state with dim 1.
"""
np.testing.assert_equal(np.isclose(schmidt_rank(bell(0), 1), 1), True)
def test_schmidt_rank_separable_density_matrix():
"""Computing Schmidt rank of separable density matrix should be 1."""
np.testing.assert_equal(schmidt_rank(np.identity(4)) == 1, True)
np.testing.assert_equal(schmidt_rank(np.identity(16)) == 1, True)
