def test_povm():
"""
Test if povm formulation works correctly by checking probabilities for
the quantum state discrimination example
"""
coeff = (sqrt(2) / (1 + sqrt(2)))
E_1 = coeff * ket2dm(basis(2, 1))
E_2 = coeff * ket2dm((basis(2, 0) - basis(2, 1)) / (sqrt(2)))
E_3 = identity(2) - E_1 - E_2
M_1 = Qobj(scipy.linalg.sqrtm(E_1))
M_2 = Qobj(scipy.linalg.sqrtm(E_2))
M_3 = Qobj(scipy.linalg.sqrtm(E_3))
ket1 = basis(2, 0)
ket2 = (basis(2, 0) + basis(2, 1)) / (sqrt(2))
dm1 = ket2dm(ket1)
dm2 = ket2dm(ket2)
M = [M_1, M_2, M_3]
_, probabilities = measurement_statistics_povm(ket1, M)
np.testing.assert_allclose(probabilities, [0, 0.293, 0.707], 0.001)
_, probabilities = measurement_statistics_povm(ket2, M)
np.testing.assert_allclose(probabilities, [0.293, 0, 0.707], 0.001)
_, probabilities = measurement_statistics_povm(dm1, M)
np.testing.assert_allclose(probabilities, [0, 0.293, 0.707], 0.001)
_, probabilities = measurement_statistics_povm(dm2, M)
np.testing.assert_allclose(probabilities, [0.293, 0, 0.707], 0.001)
def test_measurement_statistics_ind(ops, state):
""" measurement_statistics_povm: projectors on basis states with targets. """
states1, probs1 = measurement_statistics_povm(
state, [tensor(op, identity(2)) for op in ops])
states2, probs2 = measurement_statistics_povm(state, ops, targets=[0])
for a, b in zip(states1, states2):
assert isequal(a, b)
np.testing.assert_almost_equal(probs1, probs2)
def test_measure(ops, state):
"""measure_povm: test on basis states using different projectors """
collapsed_states, _ = measurement_statistics_povm(state, ops)
for _ in range(10):
index, final_state = measure_povm(state, ops)
assert isequal(final_state, collapsed_states[index])
def test_measurement_statistics_povm(ops, state, final_states, probabilities):
""" measurement_statistics_povm: projectors applied to basis states. """
collapsed_states, probs = measurement_statistics_povm(state, ops)
for i, final_state in enumerate(final_states):
collapsed_state = collapsed_states[i]
if final_state:
assert isequal(collapsed_state, final_state)
else:
assert collapsed_state is None
np.testing.assert_almost_equal(probs, probabilities)