def test_mutual_information_equivalence(self):
"""Test mutual_information is same for equivalent inputs"""
for alpha, beta in [(0, 0), (0, 0.25), (0.25, 0), (0.33, 0.33),
(0.5, 0.5), (0.75, 0.25), (0, 0.75)]:
psi = Statevector(
[alpha, beta, 0, 1j * np.sqrt(1 - alpha**2 - beta**2)])
rho = DensityMatrix(psi)
self.assertAlmostEqual(mutual_information(psi),
mutual_information(rho))
def test_mutual_information_density_matrix(self):
"""Test mutual_information function on density matrix inputs"""
# Density matrix input
rho1 = DensityMatrix([[0.5, 0, 0, 0.5], [0, 0, 0, 0], [0, 0, 0, 0], [0.5, 0, 0, 0.5]])
rho2 = DensityMatrix([[0, 0, 0, 0], [0, 0.5, -0.5j, 0], [0, 0.5j, 0.5, 0], [0, 0, 0, 0]])
self.assertAlmostEqual(mutual_information(rho1), 2)
self.assertAlmostEqual(mutual_information(rho2), 2)
# List input
rho = [[0.5, 0.5, 0, 0], [0.5, 0.5, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
self.assertEqual(mutual_information(rho), 0)
# Array input
rho = np.diag([0.25, 0.25, 0.25, 0.25])
self.assertEqual(mutual_information(rho), 0)
def discord(rho, qubit=0):
"""
The quantum discord between two qubits
Quantum discord is defined in Phys. Rev. Lett. 88, 017901 (2001).
We use base 2 for log.
Args:
rho (Array): a two-qubit density operator
qubit (int): 0 or 1, the qubit on which the measurement is done (default 0)
Return:
float: quantum discord, between [0, 1]
"""
return (mutual_information(rho, 2) / np.log(2) -
classical_correlation(rho, qubit=qubit))
def test_mutual_information_statevector(self):
"""Test mutual_information function on statevector inputs"""
# Statevector input
psi = Statevector([0.70710678118654746, 0, 0, -0.70710678118654746j])
self.assertAlmostEqual(mutual_information(psi), 2)
# List input
psi = [1, 0, 0, 0]
self.assertAlmostEqual(mutual_information(psi), 0)
# Array input
psi = np.array([0.5, 0.5, 0.5, 0.5])
self.assertAlmostEqual(mutual_information(psi), 0)
# Larger than 2 qubit input
psi_ls = [0.70710678118654746] + (14 * [0]) + [0.70710678118654746j]
psi = Statevector(psi_ls, dims=(2, 8))
self.assertAlmostEqual(mutual_information(psi), 2)
psi = Statevector(psi_ls, dims=(4, 4))
self.assertAlmostEqual(mutual_information(psi), 2)
psi = Statevector(psi_ls, dims=(8, 2))
self.assertAlmostEqual(mutual_information(psi), 2)