def quantum_teleportation(alice_state):
# Get operators we will need
CNOT = qc.CNOT()
H = qc.Hadamard()
X = qc.PauliX()
Z = qc.PauliZ()
# The prepared, shared Bell state
bell = qc.bell_state(0, 0)
# The whole state vector
state = alice_state * bell
# Apply CNOT and Hadamard gate
state = CNOT(state, qubit_indices=[0, 1])
state = H(state, qubit_indices=[0])
# Measure the first two bits
# The only uncollapsed part of the state vector is Bob's
M1, M2 = state.measure(qubit_indices=[0, 1], remove=True)
# Apply X and/or Z gates to third qubit depending on measurements
if M2:
state = X(state)
if M1:
state = Z(state)
return state
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_bell_state_measurement2(self):
state = qc.bell_state(0, 0)
rho1 = qc.DensityOperator.from_ensemble([state])
idx = np.random.randint(2)
m = rho1.measure(qubit_indices=[idx], remove=True)[0]
state = qc.bitstring(m)
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 superdense_coding(bit_1, bit_2):
# Get operators we will need
CNOT = qc.CNOT()
H = qc.Hadamard()
X = qc.PauliX()
Z = qc.PauliZ()
# The prepared, shared Bell state
# Initially, half is in Alice's possession, and half in Bob's
phi = qc.bell_state(0, 0)
# Alice manipulates her qubit
if bit_2:
phi = X(phi, qubit_indices=[0])
if bit_1:
phi = Z(phi, qubit_indices=[0])
# Bob decodes the two bits
phi = CNOT(phi)
phi = H(phi, qubit_indices=[0])
measurements = phi.measure()
return measurements
def test_bell_state_unit_length(self):
for x, y in product([0, 1], repeat=2):
state = qc.bell_state(x, y)
diff = abs(state.probabilities.sum() - 1)
self.assertLess(diff, epsilon)
def test_bell_state_example(self):
for x, y in product([0, 1], repeat=2):
state1 = qc.bell_state(x, y)
state2 = produce_bell_states.bell_state(x, y)
diff = max_absolute_difference(state1, state2)
self.assertLess(diff, epsilon)