def test_ginibre_has_correct_second_moment():
# Numerically calculate Eq. 3.20 from
# Zyczkowski and Sommers, J. Phys. A: Math. Gen. 34 7111, (2001)
#
# <Tr[rho^2])_{D,K} = ( D + K ) / ( D * K + 1 )
#
# D is dimension of Hilbert space and K is rank of state matrix
N_avg = 5000
K = 2
D = 2
avg_purity = 0
for idx in range(0, N_avg):
rho = rand_ops.ginibre_state_matrix(D, K)
avg_purity += np.trace(np.matmul(rho, rho)) / N_avg
ans = (D + K) / (D * K + 1)
assert np.absolute(avg_purity - ans) < 1e-2
D = 3
avg_purity = 0
for idx in range(0, N_avg):
rho = rand_ops.ginibre_state_matrix(D, K)
avg_purity += np.trace(np.matmul(rho, rho)) / N_avg
ans = (D + K) / (D * K + 1)
assert np.absolute(avg_purity - ans) < 1e-2
def test_ginibre_is_positive_operator():
N_avg = 10
K = 2
D = 2
eigenvallist = []
for idx in range(0, N_avg):
eigenval = la.eig(rand_ops.ginibre_state_matrix(D, K))[0]
eigenvallist += [eigenval]
eigenvalues = np.asarray(eigenvallist)
eigenvalues = eigenvalues.reshape(1, D * N_avg)
assert np.max(np.absolute(np.imag(eigenvalues))) < 1e-10
assert np.min(np.real(eigenvalues)) >= -1e-10
D = 3
eigenvallist = []
for idx in range(0, N_avg):
eigenval = la.eig(rand_ops.ginibre_state_matrix(D, K))[0]
eigenvallist += [eigenval]
eigenvalues = np.asarray(eigenvallist)
eigenvalues = eigenvalues.reshape(1, D * N_avg)
assert np.max(np.absolute(np.imag(eigenvalues))) < 1e-10
assert np.min(np.real(eigenvalues)) >= -1e-10
def test_ginibre_is_trace_one():
N_avg = 100
K = 2
D = 2
avg_trace = 0
for idx in range(0, N_avg):
avg_trace += np.trace(rand_ops.ginibre_state_matrix(D, K)) / N_avg
assert avg_trace <= 1 + 1e-10
assert avg_trace >= 1 - 1e-10