def test_simple(self):
Z = qu.pauli('Z')
P = qu.projector(Z & Z)
uu = qu.dop(qu.up()) & qu.dop(qu.up())
dd = qu.dop(qu.down()) & qu.dop(qu.down())
assert_allclose(P, uu + dd)
assert qu.expec(P, qu.bell_state('phi+')) == pytest.approx(1.0)
assert qu.expec(P, qu.bell_state('psi+')) == pytest.approx(0.0)
def test_block2_no_self_ent(self):
p = qu.bell_state('phi+') & qu.bell_state('phi+')
ecm = qu.ent_cross_matrix(p,
ent_fn=qu.logneg,
calc_self_ent=False,
sz_blc=2)
assert_allclose(ecm[0, 1], 0)
assert_allclose(ecm[0, 0], np.nan)
assert_allclose(ecm[1, 0], 0)
def test_reuse_precomp(self):
cfn = qu.correlation(None,
qu.pauli('z'),
qu.pauli('z'),
0,
1,
dims=[2, 2],
precomp_func=True)
assert_allclose(cfn(qu.bell_state('psi-')), -1.0)
assert_allclose(cfn(qu.bell_state('phi+')), 1.0)
def test_block2_upscale(self):
p = bell_state('phi+') & bell_state('phi+')
ecm = ent_cross_matrix(p, ent_fn=logneg, calc_self_ent=False, sz_blc=2)
assert ecm.shape == (2, 2)
ecm = ent_cross_matrix(p,
ent_fn=logneg,
calc_self_ent=False,
sz_blc=2,
upscale=True)
assert ecm.shape == (4, 4)
def test_entangled_permute(self):
dims = [2, 2, 2]
a = qu.bell_state(0) & qu.up()
assert_allclose(qu.mutinf_subsys(a, dims, 0, 1), 2.)
b = qu.permute(a, dims, [1, 2, 0])
assert_allclose(qu.mutinf_subsys(b, dims, 0, 1), 0., atol=1e-12)
assert_allclose(qu.mutinf_subsys(b, dims, 0, 2), 2.)
def test_bell_state(self):
p = bell_state('psi-')
assert_allclose(schmidt_gap(p, [2, 2], 0), 0.0)
p = up() & down()
assert_allclose(schmidt_gap(p, [2, 2], 0), 1.0)
p = rand_ket(2**3)
assert 0 < schmidt_gap(p, [2] * 3, sysa=[0, 1]) < 1.0
def test_bell_state(self):
p = qu.bell_state('psi-')
assert_allclose(qu.schmidt_gap(p, [2, 2], 0), 0.0)
p = qu.up() & qu.down()
assert_allclose(qu.schmidt_gap(p, [2, 2], 0), 1.0)
p = qu.rand_ket(2**3)
assert 0 < qu.schmidt_gap(p, [2] * 3, sysa=[0, 1]) < 1.0
def test_partial_transpose(self):
a = bell_state(0, qtype='dop')
b = partial_transpose(a)
assert isinstance(b, np.matrix)
assert_allclose(
b,
[[0, 0, 0, -0.5], [0, 0.5, 0, 0], [0, 0, 0.5, 0], [-0.5, 0, 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_partial_transpose(self):
a = qu.bell_state(0, qtype='dop')
b = qu.partial_transpose(a)
assert isinstance(b, qu.qarray)
assert_allclose(
b,
np.array([[0, 0, 0, -0.5], [0, 0.5, 0, 0], [0, 0, 0.5, 0],
[-0.5, 0, 0, 0]]))
def test_bell_states(self):
for s, dic in zip(("psi-", "psi+", "phi+", "phi-"), ({
"qtype": 'dop'
}, {}, {
"sparse": True
}, {})):
p = bell_state(s, **dic)
assert_allclose(expec(p, p), 1.0)
pa = ptr(p, [2, 2], 0)
assert_allclose(expec(pa, pa), 0.5)
def test_entangled(self, s, ct, pre_c):
p = qu.bell_state('psi-')
c = qu.correlation(p,
qu.pauli(s),
qu.pauli(s),
0,
1,
precomp_func=pre_c)
c = c(p) if pre_c else c
assert_allclose(c, ct)
def test_mixed(self):
rho = qu.dop(qu.bell_state('psi-'))
IZ = qu.pauli('I') & qu.pauli('Z')
ZI = qu.pauli('Z') & qu.pauli('I')
res, rho_after = qu.measure(rho, IZ)
# normalized
assert qu.tr(rho_after) == pytest.approx(1.0)
# anticorrelated
assert qu.expectation(rho_after, IZ) == pytest.approx(res)
assert qu.expectation(rho_after, ZI) == pytest.approx(-res)
assert isinstance(rho_after, qu.qarray)
def test_pure(self):
psi = qu.bell_state('psi-')
IZ = qu.pauli('I') & qu.pauli('Z')
ZI = qu.pauli('Z') & qu.pauli('I')
res, psi_after = qu.measure(psi, IZ)
# normalized
assert qu.expectation(psi_after, psi_after) == pytest.approx(1.0)
# anticorrelated
assert qu.expectation(psi_after, IZ) == pytest.approx(res)
assert qu.expectation(psi_after, ZI) == pytest.approx(-res)
assert isinstance(psi_after, qu.qarray)
def test_owci(self):
a = qu.qu([1, 0], qtype='op')
b = qu.qu([0, 1], qtype='op')
for _ in (0, 1, 2, 3):
p = qu.rand_product_state(2)
ci = qu.one_way_classical_information(p @ p.H, [a, b])
assert_allclose(ci, 0., atol=1e-12)
for i in (0, 1, 2, 3):
p = qu.bell_state(i)
ci = qu.one_way_classical_information(p @ p.H, [a, b])
assert_allclose(ci, 1., atol=1e-12)
def test_bell_states(self, qtype, bs):
p = qu.bell_state(bs, qtype=qtype)
assert qu.logneg(p) > 1.0 - 1e-14
def test_d2(self):
rho = qu.eye(2) / 2
psi = qu.purify(rho)
assert qu.expec(psi, qu.bell_state('phi+')) > 1 - 1e-14
def test_bell_state(self, bs, pre_c):
p = qu.bell_state(bs)
qids = qu.qid(p, dims=[2, 2], inds=[0, 1], precomp_func=pre_c)
assert_allclose(qids(p) if pre_c else qids, [3, 3])
def test_entropy_mixed(self):
a = 0.5 * (qu.bell_state(1, qtype='dop') +
qu.bell_state(2, qtype='dop'))
assert_allclose(1.0, qu.entropy(a), atol=1e-12)
def test_block2(self):
p = qu.bell_state('phi+') & qu.bell_state('phi+')
ecm = qu.ent_cross_matrix(p, ent_fn=qu.logneg, sz_blc=2)
assert_allclose(ecm[1, 1], 0)
assert_allclose(ecm[0, 1], 0)
assert_allclose(ecm[1, 0], 0)
def test_bell_state_no_self_ent(self):
p = qu.bell_state('phi+')
ecm = qu.ent_cross_matrix(p,
ent_fn=qu.concurrence,
calc_self_ent=False)
assert_allclose(ecm, [[np.nan, 1], [1, np.nan]])
def test_bell_state(self):
p = qu.bell_state('phi+')
ecm = qu.ent_cross_matrix(p, ent_fn=qu.concurrence, calc_self_ent=True)
assert_allclose(ecm, [[1, 1], [1, 1]])
def test_pauli_correlations_no_sum_abs(self, pre_c):
p = qu.bell_state('psi-')
ct = qu.pauli_correlations(p, sum_abs=False, precomp_func=pre_c)
assert_allclose(list(c(p) for c in ct) if pre_c else ct, (-1, -1, -1))
def test_pauli_correlations_sum_abs(self, pre_c):
p = qu.bell_state('psi-')
ct = qu.pauli_correlations(p, sum_abs=True, precomp_func=pre_c)
ct = ct(p) if pre_c else ct
assert_allclose(ct, 3.0)
def test_entropy_pure(self):
a = qu.bell_state(1, qtype='dop')
assert_allclose(0.0, qu.entropy(a), atol=1e-12)
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_partial_trace_bell_states(self):
for lab in ('psi-', 'psi+', 'phi-', 'phi+'):
psi = qu.bell_state(lab, qtype='dop')
rhoa = qu.partial_trace(psi, [2, 2], 0)
assert_allclose(rhoa, qu.eye(2) / 2)
def test_simple(self, qtype, bs):
p = qu.bell_state(bs, qtype=qtype)
assert qu.negativity(p) > 0.5 - 1e-14
def test_bell_state(self):
a = qu.bell_state('psi-', sparse=True)
b = qu.core._trace_keep(a @ a.H, [2, 2], 0)
assert_allclose(b, qu.eye(2) / 2)
b = qu.core._trace_keep(a @ a.H, [2, 2], 1)
assert_allclose(b, qu.eye(2) / 2)
def test_bell_states(self, qtype, bs):
p = qu.bell_state(bs, qtype=qtype)
assert qu.concurrence(p) > 1.0 - 1e-14