def case(S, n_trials=50):
S = to_super(S)
left_dims, right_dims = S.dims
# Assume for the purposes of the test that S maps square operators to square operators.
in_dim = np.prod(right_dims[0])
out_dim = np.prod(left_dims[0])
S_dual = to_super(S.dual_chan())
primals = []
duals = []
for idx_trial in range(n_trials):
X = rand_dm_ginibre(out_dim)
X.dims = left_dims
X = operator_to_vector(X)
Y = rand_dm_ginibre(in_dim)
Y.dims = right_dims
Y = operator_to_vector(Y)
primals.append((X.dag() * S * Y)[0, 0])
duals.append((X.dag() * S_dual.dag() * Y)[0, 0])
np.testing.assert_array_almost_equal(primals, duals)
def case(S, n_trials=50):
S = to_super(S)
left_dims, right_dims = S.dims
# Assume for the purposes of the test that S maps square operators to square operators.
in_dim = np.prod(right_dims[0])
out_dim = np.prod(left_dims[0])
S_dual = to_super(S.dual_chan())
primals = []
duals = []
for idx_trial in range(n_trials):
X = rand_dm_ginibre(out_dim)
X.dims = left_dims
X = operator_to_vector(X)
Y = rand_dm_ginibre(in_dim)
Y.dims = right_dims
Y = operator_to_vector(Y)
primals.append((X.dag() * S * Y)[0, 0])
duals.append((X.dag() * S_dual.dag() * Y)[0, 0])
np.testing.assert_array_almost_equal(primals, duals)
def test_dual_channel(sub_dimensions, n_trials=50):
"""
Qobj: dual_chan() preserves inner products with arbitrary density ops.
"""
S = rand_super_bcsz(np.prod(sub_dimensions))
S.dims = [[sub_dimensions, sub_dimensions],
[sub_dimensions, sub_dimensions]]
S = to_super(S)
left_dims, right_dims = S.dims
# Assume for the purposes of the test that S maps square operators to
# square operators.
in_dim = np.prod(right_dims[0])
out_dim = np.prod(left_dims[0])
S_dual = to_super(S.dual_chan())
primals = []
duals = []
for _ in [None] * n_trials:
X = rand_dm_ginibre(out_dim)
X.dims = left_dims
X = operator_to_vector(X)
Y = rand_dm_ginibre(in_dim)
Y.dims = right_dims
Y = operator_to_vector(Y)
primals.append((X.dag() * S * Y)[0, 0])
duals.append((X.dag() * S_dual.dag() * Y)[0, 0])
np.testing.assert_array_almost_equal(primals, duals)
def test_fidelity_bounded_mixedmixed(tol=1e-7):
"""
Metrics: Fidelity of mixed states within [0, 1].
"""
for _ in range(10):
rho = rand_dm_ginibre(11)
sigma = rand_dm_ginibre(11)
F = fidelity(rho, sigma)
assert_(-tol <= F <= 1 + tol)
def test_fidelity_bounded_mixedmixed(tol=1e-7):
"""
Metrics: Fidelity of mixed states within [0, 1].
"""
for _ in range(10):
rho = rand_dm_ginibre(11)
sigma = rand_dm_ginibre(11)
F = fidelity(rho, sigma)
assert_(-tol <= F <= 1 + tol)
def test_call():
"""
Test Qobj: Call
"""
# Make test objects.
psi = rand_ket(3)
rho = rand_dm_ginibre(3)
U = rand_unitary(3)
S = rand_super_bcsz(3)
# Case 0: oper(ket).
assert U(psi) == U * psi
# Case 1: oper(oper). Should raise TypeError.
with expect_exception(TypeError):
U(rho)
# Case 2: super(ket).
assert S(psi) == vector_to_operator(S * operator_to_vector(ket2dm(psi)))
# Case 3: super(oper).
assert S(rho) == vector_to_operator(S * operator_to_vector(rho))
# Case 4: super(super). Should raise TypeError.
with expect_exception(TypeError):
S(S)
def test_call():
"""
Test Qobj: Call
"""
# Make test objects.
psi = rand_ket(3)
rho = rand_dm_ginibre(3)
U = rand_unitary(3)
S = rand_super_bcsz(3)
# Case 0: oper(ket).
assert U(psi) == U * psi
# Case 1: oper(oper). Should raise TypeError.
with expect_exception(TypeError):
U(rho)
# Case 2: super(ket).
assert S(psi) == vector_to_operator(S * operator_to_vector(ket2dm(psi)))
# Case 3: super(oper).
assert S(rho) == vector_to_operator(S * operator_to_vector(rho))
# Case 4: super(super). Should raise TypeError.
with expect_exception(TypeError):
S(S)
def test_rand_dm_ginibre_rank():
"""
Random Qobjs: Ginibre-random density ops have correct rank.
"""
rho = rand_dm_ginibre(5, rank=3)
rank = sum([abs(E) >= 1e-10 for E in rho.eigenenergies()])
assert_(rank == 3)
def test_fidelity_bounded_puremixed(tol=1e-7):
"""
Metrics: Fidelity of pure states against mixed states within [0, 1].
"""
for _ in range(10):
psi = rand_ket_haar(11)
sigma = rand_dm_ginibre(11)
F = fidelity(psi, sigma)
assert_(-tol <= F <= 1 + tol)
def test_fidelity_bounded_puremixed(tol=1e-7):
"""
Metrics: Fidelity of pure states against mixed states within [0, 1].
"""
for _ in range(10):
psi = rand_ket_haar(11)
sigma = rand_dm_ginibre(11)
F = fidelity(psi, sigma)
assert_(-tol <= F <= 1 + tol)
def test_stinespring_agrees(self, thresh=1e-10):
"""
Stinespring: Partial Tr over pair agrees w/ supermatrix.
"""
def case(map, state):
S = to_super(map)
A, B = to_stinespring(map)
q1 = vector_to_operator(S * operator_to_vector(state))
# FIXME: problem if Kraus index is implicitly
# ptraced!
q2 = (A * state * B.dag()).ptrace((0, ))
assert_((q1 - q2).norm('tr') <= thresh)
for idx in range(4):
case(rand_super_bcsz(2), rand_dm_ginibre(2))
def test_stinespring_agrees(self, dimension):
"""
Stinespring: Partial Tr over pair agrees w/ supermatrix.
"""
map = rand_super_bcsz(dimension)
state = rand_dm_ginibre(dimension)
S = to_super(map)
A, B = to_stinespring(map)
q1 = vector_to_operator(S * operator_to_vector(state))
# FIXME: problem if Kraus index is implicitly
# ptraced!
q2 = (A * state * B.dag()).ptrace((0, ))
assert (q1 - q2).norm('tr') <= tol
def test_stinespring_agrees(self, thresh=1e-10):
"""
Stinespring: Partial Tr over pair agrees w/ supermatrix.
"""
def case(map, state):
S = to_super(map)
A, B = to_stinespring(map)
q1 = vector_to_operator(
S * operator_to_vector(state)
)
# FIXME: problem if Kraus index is implicitly
# ptraced!
q2 = (A * state * B.dag()).ptrace((0,))
assert_((q1 - q2).norm('tr') <= thresh)
for idx in range(4):
yield case, rand_super_bcsz(2), rand_dm_ginibre(2)
