def test_base_2_or_e(self):
rho = qutip.ket2dm(qutip.ket("00"))
sigma = rho + qutip.ket2dm(qutip.ket("01"))
sigma = sigma.unit()
assert (qutip.entropy_relative(rho, sigma) == pytest.approx(np.log(2)))
assert (qutip.entropy_relative(rho, sigma,
base=np.e) == pytest.approx(0.69314718))
assert qutip.entropy_relative(rho, sigma, base=2) == pytest.approx(1)
def test_rho_and_sigma_have_different_shape_and_dims(self):
# test different shape and dims
rho = qutip.ket("00")
sigma = qutip.ket("0")
with pytest.raises(ValueError) as exc:
qutip.entropy_relative(rho, sigma)
assert str(exc.value) == "Inputs must have the same shape and dims."
# test same shape, difference dims
rho = qutip.basis([2, 3], [0, 0])
sigma = qutip.basis([3, 2], [0, 0])
with pytest.raises(ValueError) as exc:
qutip.entropy_relative(rho, sigma)
assert str(exc.value) == "Inputs must have the same shape and dims."
def test_random_rho_sigma(self):
rho = qutip.rand_dm(8, pure=False)
sigma = qutip.rand_dm(8, pure=False)
rel = qutip.entropy_relative(rho, sigma)
assert rel >= 0
assert rel == pytest.approx(
self._simple_relative_entropy_implementation(rho, sigma, np.log))
def test_density_matrices_with_non_real_eigenvalues(self):
rho = qutip.ket2dm(qutip.ket("00"))
sigma = qutip.ket2dm(qutip.ket("01"))
with pytest.raises(ValueError) as exc:
qutip.entropy_relative(rho + 1j, sigma)
assert str(exc.value) == "Input rho has non-real eigenvalues."
with pytest.raises(ValueError) as exc:
qutip.entropy_relative(rho - 1j, sigma)
assert str(exc.value) == "Input rho has non-real eigenvalues."
with pytest.raises(ValueError) as exc:
qutip.entropy_relative(rho, sigma + 1j)
assert str(exc.value) == "Input sigma has non-real eigenvalues."
with pytest.raises(ValueError) as exc:
qutip.entropy_relative(rho, sigma - 1j)
assert str(exc.value) == "Input sigma has non-real eigenvalues."
def test_rho_or_sigma_not_oper(self):
rho = qutip.bra("00")
sigma = qutip.bra("01")
with pytest.raises(TypeError) as exc:
qutip.entropy_relative(rho.dag(), sigma)
assert str(exc.value) == "Inputs must be density matrices."
with pytest.raises(TypeError) as exc:
qutip.entropy_relative(rho, sigma.dag())
assert str(exc.value) == "Inputs must be density matrices."
with pytest.raises(TypeError) as exc:
qutip.entropy_relative(rho, sigma)
assert str(exc.value) == "Inputs must be density matrices."
def test_random_dm_with_self(self):
rho = qutip.rand_dm(8, pure=False)
rel = qutip.entropy_relative(rho, rho)
assert abs(rel) < 1e-13
def test_pure_vs_maximally_mixed_state(self):
rho = qutip.ket("00")
sigma = sum(
qutip.ket2dm(qutip.ket(psi))
for psi in ["00", "01", "10", "11"]).unit()
assert qutip.entropy_relative(rho, sigma, base=2) == pytest.approx(2)
def test_infinite_relative_entropy(self):
rho = qutip.ket("00")
sigma = qutip.ket("01")
assert qutip.entropy_relative(rho, sigma) == np.inf
def test_base_not_2_or_e(self):
rho = qutip.ket("00")
sigma = qutip.ket("01")
with pytest.raises(ValueError) as exc:
qutip.entropy_relative(rho, sigma, base=3)
assert str(exc.value) == "Base must be 2 or e."