def test_schmidt_examples(self):
self.assertEqual(qc.bell_state().schmidt_number(indices=[0]), 2)
self.assertEqual(
qc.positive_superposition(d=2).schmidt_number(indices=[0]), 1)
x = (qc.bitstring(0, 0) + qc.bitstring(0, 1) +
qc.bitstring(1, 0)) / np.sqrt(3)
self.assertEqual(x.schmidt_number(indices=[0]), 2)
def test_positive_superposition_measurement(self):
state = qc.positive_superposition()
rho1 = qc.DensityOperator.from_ensemble([state])
measurement = rho1.measure()[0]
state = qc.bitstring(measurement)
rho2 = qc.DensityOperator.from_ensemble([state])
assert_allclose(rho1._t, rho2._t)
def test_unitarily_unchanged(self):
num_tests = 10
for test_i in range(num_tests):
x = qc.positive_superposition(d=2)
U = random_unitary_operator(d=1) * random_unitary_operator(d=1)
self.assertEqual(U(x).schmidt_number(indices=[0]), 1)
x = qc.bell_state()
U = random_unitary_operator(d=1) * random_unitary_operator(d=1)
self.assertEqual(U(x).schmidt_number(indices=[0]), 2)
def test_superposition(self):
x = qc.positive_superposition()
y1 = (qc.zeros() + qc.ones()) / np.sqrt(2)
y2 = (qc.zeros() + qc.ones()) * (1 / np.sqrt(2))
y3 = (1 / np.sqrt(2)) * (qc.ones() + qc.zeros())
y4 = (1 / np.sqrt(2)) * qc.ones() + qc.zeros() / np.sqrt(2)
self.assertLess(max_absolute_difference(y1, x), epsilon)
self.assertLess(max_absolute_difference(y2, x), epsilon)
self.assertLess(max_absolute_difference(y3, x), epsilon)
self.assertLess(max_absolute_difference(y4, x), epsilon)
self.assertLess(
max_absolute_difference(np.sqrt(2) * x - qc.ones(), qc.zeros()),
epsilon)