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_depolarize(self, stack):
rho = qu.rand_rho(2)
I, X, Y, Z = (qu.pauli(s) for s in 'IXYZ')
es = [qu.expec(rho, A) for A in (X, Y, Z)]
p = 0.1
Ek = [(1 - p)**0.5 * I, (p / 3)**0.5 * X, (p / 3)**0.5 * Y,
(p / 3)**0.5 * Z]
if stack:
Ek = np.stack(Ek, axis=0)
sigma = qu.kraus_op(rho, Ek, check=True)
es2 = [qu.expec(sigma, A) for A in (X, Y, Z)]
assert qu.tr(sigma) == pytest.approx(1.0)
assert all(abs(e2) < abs(e) for e, e2 in zip(es, es2))
sig_exp = sum(E @ rho @ qu.dag(E) for E in Ek)
assert_allclose(sig_exp, sigma)
def test_multisubsystem(self):
qu.seed_rand(42)
dims = [2, 2, 2]
IIX = qu.ikron(qu.rand_herm(2), dims, 2)
dcmp = qu.pauli_decomp(IIX, mode='c')
for p, x in dcmp.items():
if x == 0j:
assert (p[0] != 'I') or (p[1] != 'I')
else:
assert p[0] == p[1] == 'I'
K = qu.rand_iso(3 * 4, 4).reshape(3, 4, 4)
KIIXK = qu.kraus_op(IIX, K, dims=dims, where=[0, 2])
dcmp = qu.pauli_decomp(KIIXK, mode='c')
for p, x in dcmp.items():
if x == 0j:
assert p[1] != 'I'
else:
assert p[1] == 'I'