def fock_amplitudes_one_mode(alpha, cov, cutoff):
""" Returns the Fock space density matrix of gaussian state characterized
by a complex displacement alpha and a (symmetric) covariance matrix
The Fock ladder ladder goes from 0 to cutoff-1"""
r = 2 * np.array([alpha.real, alpha.imag])
if is_pure_cov(cov):
psi = state_vector(r, cov, normalize=True, cutoff=cutoff)
rho = np.outer(psi, psi.conj())
return rho
return density_matrix(r, cov, normalize=True, cutoff=cutoff)
def test_state_vector_coherent():
""" Tests state vector for a coherent state """
cutoff = 5
cov = np.identity(2)
mu = np.array([1.0, 2.0])
beta = Beta(mu)
alpha = beta[0]
exact = np.array([(np.exp(-0.5 * np.abs(alpha) ** 2) * alpha ** i / np.sqrt(np.math.factorial(i))) for i in range(cutoff)])
num = state_vector(mu, cov, cutoff=cutoff)
assert np.allclose(exact, num)
def test_state_vector_two_mode_squeezed():
""" Tests state_vector for a two mode squeezed vacuum state """
nbar = 1.0
cutoff = 5
phase = np.pi / 8
r = np.arcsinh(np.sqrt(nbar))
cov = two_mode_squeezing(2 * r, phase)
mu = np.zeros([4], dtype=np.complex)
exact = np.array([(np.exp(1j * i * phase) * (nbar / (1.0 + nbar)) ** (i / 2) / np.sqrt(1.0 + nbar)) for i in range(cutoff)])
psi = state_vector(mu, cov, cutoff=cutoff)
expected = np.diag(exact)
assert np.allclose(psi, expected)
def test_state_vector_two_mode_squeezed_post_normalize():
""" Tests state_vector for a two mode squeezed vacuum state """
nbar = 1.0
cutoff = 5
phase = np.pi / 8
r = np.arcsinh(np.sqrt(nbar))
cov = two_mode_squeezing(2 * r, phase)
mu = np.zeros([4], dtype=np.complex)
exact = np.diag(np.array([(np.exp(1j * i * phase) * (nbar / (1.0 + nbar)) ** (i / 2) / np.sqrt(1.0 + nbar)) for i in range(cutoff)]))
val = 2
post_select = {0: val}
psi = state_vector(mu, cov, cutoff=cutoff, post_select=post_select, normalize=True)
expected = exact[val]
expected = expected / np.linalg.norm(expected)
assert np.allclose(psi, expected)
def test_cubic_phase():
"""Test that all the possible ways of obtaining a cubic phase state using the different methods agree"""
mu = np.array([
-0.50047867, 0.37373598, 0.01421683, 0.26999427, 0.04450994, 0.01903583
])
cov = np.array([
[
1.57884241, 0.81035494, 1.03468307, 1.14908791, 0.09179507,
-0.11893174
],
[
0.81035494, 1.06942863, 0.89359234, 0.20145142, 0.16202296,
0.4578259
],
[
1.03468307, 0.89359234, 1.87560498, 0.16915661, 1.0836528,
-0.09405278
],
[
1.14908791, 0.20145142, 0.16915661, 2.37765137, -0.93543385,
-0.6544286
],
[
0.09179507, 0.16202296, 1.0836528, -0.93543385, 2.78903152,
-0.76519088
],
[
-0.11893174, 0.4578259, -0.09405278, -0.6544286, -0.76519088,
1.51724222
],
])
cutoff = 7
# the Fock state measurement of mode 0 to be post-selected
m1 = 1
# the Fock state measurement of mode 1 to be post-selected
m2 = 2
psi = state_vector(mu,
cov,
post_select={
0: m1,
1: m2
},
cutoff=cutoff,
hbar=2)
psi_c = state_vector(mu, cov, cutoff=cutoff, hbar=2)[m1, m2, :]
rho = density_matrix(mu,
cov,
post_select={
0: m1,
1: m2
},
cutoff=cutoff,
hbar=2)
rho_c = density_matrix(mu, cov, cutoff=cutoff, hbar=2)[m1, m2, :, m1,
m2, :]
assert np.allclose(np.outer(psi, psi.conj()), rho)
assert np.allclose(np.outer(psi_c, psi_c.conj()), rho)
assert np.allclose(rho_c, rho)
def get_state_vector(self):
return quantum.state_vector(self.mu, self.cov)
