def random_cov(num_modes=200, pure=False, nonclassical=True):
r"""Creates a random covariance matrix for testing.
Args:
num_modes (int): number of modes
pure (bool): Gaussian state is pure
nonclassical (bool): Gaussian state is nonclassical
Returns:
(array): a covariance matrix
"""
M = num_modes
O = interferometer(random_interferometer(M))
eta = 1 if pure else 0.123
r = 1.234
if nonclassical:
# squeezed inputs
cov_in = np.diag(np.concatenate([np.exp(2 * r) * np.ones(M), np.exp(-2 * r) * np.ones(M)]))
elif not nonclassical and pure:
# vacuum inputs
cov_in = np.eye(2 * M)
elif not nonclassical and not pure:
# squashed inputs
cov_in = np.diag(np.concatenate([np.exp(2 * r) * np.ones(M), np.ones(M)]))
cov_out = O @ cov_in @ O.T
_, cov = passive_transformation(
np.zeros([len(cov_out)]), cov_out, np.sqrt(eta) * np.identity(len(cov_out) // 2)
)
return cov
def test_transformation(self, tol):
"""Test that an transformation returns the correct state"""
M = 4
cov = np.arange(4 * M**2, dtype=np.float64).reshape((2 * M, 2 * M))
mu = np.arange(2 * M, dtype=np.float64)
T = np.sqrt(0.9) * M**(-0.5) * np.ones((6, M), dtype=np.float64)
mu_out, cov_out = symplectic.passive_transformation(mu, cov, T)
# fmt:off
expected_mu = np.array([
2.84604989, 2.84604989, 2.84604989, 2.84604989, 2.84604989,
2.84604989, 10.43551628, 10.43551628, 10.43551628, 10.43551628,
10.43551628, 10.43551628
])
expected_cov = np.array([
[48.7, 47.7, 47.7, 47.7, 47.7, 47.7, 63., 63., 63., 63., 63., 63.],
[47.7, 48.7, 47.7, 47.7, 47.7, 47.7, 63., 63., 63., 63., 63., 63.],
[47.7, 47.7, 48.7, 47.7, 47.7, 47.7, 63., 63., 63., 63., 63., 63.],
[47.7, 47.7, 47.7, 48.7, 47.7, 47.7, 63., 63., 63., 63., 63., 63.],
[47.7, 47.7, 47.7, 47.7, 48.7, 47.7, 63., 63., 63., 63., 63., 63.],
[47.7, 47.7, 47.7, 47.7, 47.7, 48.7, 63., 63., 63., 63., 63., 63.],
[
163.8, 163.8, 163.8, 163.8, 163.8, 163.8, 178.3, 177.3, 177.3,
177.3, 177.3, 177.3
],
[
163.8, 163.8, 163.8, 163.8, 163.8, 163.8, 177.3, 178.3, 177.3,
177.3, 177.3, 177.3
],
[
163.8, 163.8, 163.8, 163.8, 163.8, 163.8, 177.3, 177.3, 178.3,
177.3, 177.3, 177.3
],
[
163.8, 163.8, 163.8, 163.8, 163.8, 163.8, 177.3, 177.3, 177.3,
178.3, 177.3, 177.3
],
[
163.8, 163.8, 163.8, 163.8, 163.8, 163.8, 177.3, 177.3, 177.3,
177.3, 178.3, 177.3
],
[
163.8, 163.8, 163.8, 163.8, 163.8, 163.8, 177.3, 177.3, 177.3,
177.3, 177.3, 178.3
]
])
# fmt:on
assert np.allclose(mu_out, expected_mu, atol=tol, rtol=0)
assert np.allclose(cov_out, expected_cov, atol=tol, rtol=0)
def test_hbar(self, hbar, tol):
"""test that the output is a valid covariance matrix, even when not square"""
M = 4
a = np.arange(4 * M**2, dtype=np.float64).reshape((2 * M, 2 * M))
cov = a @ a.T + np.eye(2 * M)
mu = np.arange(2 * M, dtype=np.float64)
T = np.sqrt(0.9) * M**(-0.5) * np.ones((6, M), dtype=np.float64)
_, cov_out = symplectic.passive_transformation(mu, cov, T, hbar=hbar)
assert is_valid_cov(cov_out, hbar=hbar, atol=tol, rtol=0)
def test_valid_cov(self, M, tol):
"""test that the output is a valid covariance matrix, even when not square"""
a = np.arange(4 * M**2, dtype=np.float64).reshape((2 * M, 2 * M))
cov = a @ a.T + np.eye(2 * M)
mu = np.arange(2 * M, dtype=np.float64)
T = np.sqrt(0.9) * M**(-0.5) * np.ones((6, M), dtype=np.float64)
mu_out, cov_out = symplectic.passive_transformation(mu, cov, T)
assert cov_out.shape == (12, 12)
assert len(mu_out) == 12
assert is_valid_cov(cov_out, atol=tol, rtol=0)
def test_log_negativity_two_modes(r, etaA, etaB, hbar):
"""Tests the log_negativity for two modes states following Eq. 13 of https://arxiv.org/pdf/quant-ph/0506124.pdf"""
cov = (hbar / 2) * two_mode_squeezing(2 * r, 0)
_, cov_lossy = passive_transformation(np.zeros([4]), cov, np.diag([etaA, etaB]), hbar=hbar)
cov_xpxp = xxpp_to_xpxp(cov_lossy) / (hbar / 2)
alpha = cov_xpxp[:2, :2]
gamma = cov_xpxp[2:, :2]
beta = cov_xpxp[2:, 2:]
invariant = np.linalg.det(alpha) + np.linalg.det(beta) - 2 * np.linalg.det(gamma)
detcov = np.linalg.det(cov_xpxp)
expected = -np.log(np.sqrt((invariant - np.sqrt(invariant**2 - 4 * detcov)) / 2))
obtained = log_negativity(cov_lossy, modes_A=[0], hbar=hbar)
assert np.allclose(expected, obtained)
def test_unitary(self, M, tol):
"""
test that the outputs agree with the interferometer class when
transformation is unitary
"""
a = np.arange(4 * M**2, dtype=np.float64).reshape((2 * M, 2 * M))
cov = a @ a.T + np.eye(2 * M)
mu = np.arange(2 * M, dtype=np.float64)
U = M**(-0.5) * np.fft.fft(np.eye(M))
S_U = symplectic.interferometer(U)
cov_U = S_U @ cov @ S_U.T
mu_U = S_U @ mu
mu_T, cov_T = symplectic.passive_transformation(mu, cov, U)
assert np.allclose(mu_U, mu_T, atol=tol, rtol=0)
assert np.allclose(cov_U, cov_T, atol=tol, rtol=0)