def test_rand_product_state(self):
a = rand_product_state(3)
assert a.shape[0] == 2**3
assert_almost_equal((a.H @ a)[0, 0].real, 1.0)
assert_almost_equal(mutual_information(a, [2, 2, 2], 0, 1), 0.0)
assert_almost_equal(mutual_information(a, [2, 2, 2], 1, 2), 0.0)
assert_almost_equal(mutual_information(a, [2, 2, 2], 0, 2), 0.0)
def test_mutual_information_pure_sub(self):
a = qu.up() & qu.bell_state(1)
ixy = qu.mutual_information(a, [2, 2, 2], 0, 1)
assert_allclose(0.0, ixy, atol=1e-12)
ixy = qu.mutual_information(a, [2, 2, 2], 0, 2)
assert_allclose(0.0, ixy, atol=1e-12)
ixy = qu.mutual_information(a, [2, 2, 2], 2, 1)
assert_allclose(2.0, ixy, atol=1e-12)
def test_quantum_discord_pure(self):
for _ in range(10):
p = qu.rand_ket(4)
p = p @ p.H
iab = qu.mutual_information(p)
qd = qu.quantum_discord(p)
assert_allclose(iab / 2, qd)
def test_mutinf_subsys_pure(self):
p = rand_ket(2**7)
dims = (2**3, 2**4)
# exact
mi0 = mutual_information(p, dims, sysa=0)
mi1 = mutinf_subsys(p, dims, sysa=0, sysb=1, approx_thresh=1e30)
assert_allclose(mi1, mi0)
# approx
mi2 = mutinf_subsys(p, dims, sysa=0, sysb=1, approx_thresh=1)
assert_allclose(mi1, mi2, rtol=5e-2)
def test_mutinf_subsys(self):
p = qu.rand_ket(2**9)
dims = (2**3, 2**2, 2**4)
# exact
rho_ab = qu.ptr(p, dims, [0, 2])
mi0 = qu.mutual_information(rho_ab, [8, 16])
mi1 = qu.mutinf_subsys(p, dims, sysa=0, sysb=2, approx_thresh=1e30)
assert_allclose(mi1, mi0)
# approx
mi2 = qu.mutinf_subsys(p, dims, sysa=0, sysb=2, approx_thresh=1)
assert_allclose(mi1, mi2, rtol=0.1)
def test_subsystem(self):
rho = qu.rand_rho(6)
dims = [3, 2]
I, X, Y, Z = (qu.pauli(s) for s in 'IXYZ')
mi_i = qu.mutual_information(rho, dims)
p = 0.1
Ek = [(1 - p)**0.5 * I, (p / 3)**0.5 * X, (p / 3)**0.5 * Y,
(p / 3)**0.5 * Z]
with pytest.raises(ValueError):
qu.kraus_op(rho,
qu.randn((3, 2, 2)),
check=True,
dims=dims,
where=1)
sigma = qu.kraus_op(rho, Ek, check=True, dims=dims, where=1)
mi_f = qu.mutual_information(sigma, dims)
assert mi_f < mi_i
assert qu.tr(sigma) == pytest.approx(1.0)
sig_exp = sum(
(qu.eye(3) & E) @ rho @ qu.dag(qu.eye(3) & E) for E in Ek)
assert_allclose(sig_exp, sigma)
def test_mutinf_interleave_pure(self):
p = qu.singlet() & qu.singlet()
ixy = qu.mutual_information(p, [2] * 4, sysa=(0, 2))
assert_allclose(ixy, 4)
def test_mixed_sub(self, inds):
a = qu.rand_rho(2**3)
rho_ab = qu.ptr(a, [2, 2, 2], inds)
ixy = qu.mutual_information(rho_ab, (2, 2))
assert (0 <= ixy <= 2.0)
def test_mutual_information_pure(self):
a = qu.bell_state(0)
assert_allclose(qu.mutual_information(a), 2.)
a = qu.rand_product_state(2)
assert_allclose(qu.mutual_information(a), 0., atol=1e-12)
def test_mutinf_interleave(self):
p = dop(singlet() & singlet())
ixy = mutual_information(p, [2] * 4, sysa=(0, 2))
assert_allclose(ixy, 4)
