def test_reduced_gaussian_exceptions():
"""raises an exception"""
mu = np.array([0, 0, 0, 0])
cov = np.identity(4)
with pytest.raises(ValueError, match="Provided mode is larger than the number of subsystems."):
reduced_gaussian(mu, cov, [0, 5])
def test_disp_torontonian_two_mode(scale):
"""Calculates the probability of clicking for a two mode state"""
cv = random_covariance(2)
mu = scale * (2 * np.random.rand(4) - 1)
prob_click = threshold_detection_prob(mu, cv, [1, 1])
mu0, cv0 = reduced_gaussian(mu, cv, [0])
mu1, cv1 = reduced_gaussian(mu, cv, [1])
expected = (
1
- density_matrix_element(mu0, cv0, [0], [0])
- density_matrix_element(mu1, cv1, [0], [0])
+ density_matrix_element(mu, cv, [0, 0], [0, 0])
)
assert np.allclose(expected, prob_click)
def test_reduced_gaussian_full_state():
"""returns the arguments"""
mu = np.array([0, 0, 0, 0])
cov = np.identity(4)
res = reduced_gaussian(mu, cov, list(range(2)))
assert np.all(mu == res[0])
assert np.all(cov == res[1])
def test_reduced_gaussian_two_mode():
"""test that reduced gaussian returns the correct result"""
m = 5
N = 2 * m
mu = np.arange(N)
cov = np.arange(N**2).reshape(N, N)
res = reduced_gaussian(mu, cov, [0, 2])
assert np.all(res[0] == np.array([0, 2, m, m + 2]))
def test_reduced_gaussian(n):
"""test that reduced gaussian returns the correct result"""
m = 5
N = 2 * m
mu = np.arange(N)
cov = np.arange(N ** 2).reshape(N, N)
res = reduced_gaussian(mu, cov, n)
assert np.all(res[0] == np.array([n, n + m]))
assert np.all(res[1] == np.array([[(N + 1) * n, (N + 1) * n + m], [(N + 1) * n + N * m, (N + 1) * n + N * m + m]]))
def marginals(mu: np.ndarray,
V: np.ndarray,
n_max: int,
hbar: float = 2.0) -> np.ndarray:
r"""Generate single-mode marginal distributions from the displacement vector and covariance
matrix of a Gaussian state.
**Example usage:**
>>> mu = np.array([0.00000000, 2.82842712, 0.00000000,
... 0.00000000, 0.00000000, 0.00000000])
>>> V = np.array([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0],
... [0.0, 1.0, 0.0, 0.0, 0.0, 0.0],
... [0.0, 0.0, 1.0, 0.0, 0.0, 0.0],
... [0.0, 0.0, 0.0, 1.0, 0.0, 0.0],
... [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],
... [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])
>>> n_max = 10
>>> marginals(mu, V, n_max)
array([[1.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00],
[1.35335284e-01, 2.70670567e-01, 2.70670566e-01, 1.80447044e-01,
9.02235216e-02, 3.60894085e-02, 1.20298028e-02, 3.43708650e-03,
8.59271622e-04, 1.90949249e-04],
[1.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00]])
Args:
mu (array): displacement vector
V (array): covariance matrix
n_max (int): maximum number of vibrational quanta in the distribution
hbar (float): the value of :math:`\hbar` in the commutation relation :math:`[\x,\p]=i\hbar`.
Returns:
array[list[float]]: marginal distributions
"""
if not V.shape[0] == V.shape[1]:
raise ValueError("The covariance matrix must be a square matrix")
if not len(mu) == len(V):
raise ValueError(
"The dimension of the displacement vector and the covariance matrix must be equal"
)
if n_max <= 0:
raise ValueError(
"The number of vibrational states must be larger than zero")
n_modes = len(mu) // 2
p = np.zeros((n_modes, n_max))
for mode in range(n_modes):
mui, vi = quantum.reduced_gaussian(mu, V, mode)
for i in range(n_max):
p[mode, i] = np.real(
quantum.density_matrix_element(mui, vi, [i], [i], hbar=hbar))
return p
