def test_deprecated():
density_matrix = np.array([[0.5, 0], [0, 0.5]])
with cirq.testing.assert_deprecated('density_matrix',
'state',
deadline="v0.11"):
# pylint: disable=unexpected-keyword-arg,no-value-for-parameter
_ = cirq.von_neumann_entropy(density_matrix=density_matrix)
def test_von_neumann_entropy():
# 1x1 matrix
assert cirq.von_neumann_entropy(np.array([[1]])) == 0
# An EPR pair state (|00> + |11>)(<00| + <11|)
assert (
cirq.von_neumann_entropy(0.5 * np.array([1, 0, 0, 1] * np.array([[1], [0], [0], [1]]))) == 0
)
# Maximally mixed state
# yapf: disable
assert cirq.von_neumann_entropy(np.array(
[[0.5, 0],
[0, 0.5]])) == 1
# yapf: enable
# 2x2 random unitary, each column as a ket, each ket as a density matrix,
# linear combination of the two with coefficients 0.1 and 0.9
res = cirq.testing.random_unitary(2)
first_column = res[:, 0]
first_density_matrix = 0.1 * np.outer(first_column, np.conj(first_column))
second_column = res[:, 1]
second_density_matrix = 0.9 * np.outer(second_column, np.conj(second_column))
assert np.isclose(
cirq.von_neumann_entropy(first_density_matrix + second_density_matrix), 0.4689, atol=1e-04
)
assert np.isclose(
cirq.von_neumann_entropy(np.diag([0, 0, 0.1, 0, 0.2, 0.3, 0.4, 0])), 1.8464, atol=1e-04
)
# Random NxN matrix
probs = np.random.exponential(size=N)
probs /= np.sum(probs)
mat = U @ (probs * U).T.conj()
np.testing.assert_allclose(
cirq.von_neumann_entropy(mat), -np.sum(probs * np.log(probs) / np.log(2))
)
# QuantumState object
assert (
cirq.von_neumann_entropy(cirq.quantum_state(np.array([[0.5, 0], [0, 0.5]]), qid_shape=(2,)))
== 1
)
assert (
cirq.von_neumann_entropy(
cirq.quantum_state(np.array([[0.5, 0.5], [0.5, 0.5]]), qid_shape=(2, 2))
)
== 0
)
def test_von_neumann_entropy():
# 1x1 matrix
assert cirq.von_neumann_entropy(np.array([[1]])) == 0
# An EPR pair state (|00> + |11>)(<00| + <11|)
assert cirq.von_neumann_entropy(
np.array([1, 0, 0, 1] * np.array([[1], [0], [0], [1]]))) == 0
# Maximally mixed state
# yapf: disable
assert cirq.von_neumann_entropy(np.array(
[[0.5, 0],
[0, 0.5]])) == 1
# 3x3 state
assert np.isclose(cirq.von_neumann_entropy(
np.array(
[[0.5, 0.5j, 1],
[-0.5j, 0.5, 0],
[0.7, 0.4, 0.6]])),
1.37,
atol=1e-01)
# 4X4 state
assert np.isclose(cirq.von_neumann_entropy(
np.array(
[[0.5, 0.5j, 1, 3],
[-0.5j, 0.5, 0, 4],
[0.7, 0.4, 0.6, 5],
[6, 7, 8, 9]])),
1.12,
atol=1e-01)
# yapf: enable
# 2x2 random unitary, each column as a ket, each ket as a density matrix,
# linear combination of the two with coefficients 0.1 and 0.9
res = cirq.testing.random_unitary(2)
first_column = res[:, 0]
first_density_matrix = 0.1 * np.outer(first_column, np.conj(first_column))
second_column = res[:, 1]
second_density_matrix = 0.9 * np.outer(second_column,
np.conj(second_column))
assert np.isclose(cirq.von_neumann_entropy(first_density_matrix +
second_density_matrix),
0.4689,
atol=1e-04)
assert np.isclose(cirq.von_neumann_entropy(
np.diag([0, 0, 0.1, 0, 0.2, 0.3, 0.4, 0])),
1.8464,
atol=1e-04)