def test_EntropyConditional():
"Entropy: Conditional entropy"
# test_ S(A,B|C,D)<=S(A|C)+S(B|D)
rhos = [
rand_dm(16, dims=[[2, 2, 2, 2], [2, 2, 2, 2]], pure=True)
for k in range(20)
]
for ABCD in rhos:
AC = ptrace(ABCD, [0, 2])
BD = ptrace(ABCD, [1, 3])
assert_equal(
entropy_conditional(ABCD, [2, 3]) <=
(entropy_conditional(AC, 1) + entropy_conditional(BD, 1)), True)
# test_ S(A|B,C)<=S(A|B)
rhos = [
rand_dm(8, dims=[[2, 2, 2], [2, 2, 2]], pure=True) for k in range(20)
]
for ABC in rhos:
AB = ptrace(ABC, [0, 1])
assert_equal(
entropy_conditional(ABC, [1, 2]) <= entropy_conditional(AB, 1),
True)
def test_triangle_inequality_4_qubits(self):
# S(A,B | C,D) <= S(A|C) + S(B|D)
full = qutip.rand_dm(16, dims=[[2] * 4] * 2, pure=True)
ac, bd = full.ptrace([0, 2]), full.ptrace([1, 3])
assert (qutip.entropy_conditional(full, [2, 3]) <=
(qutip.entropy_conditional(ac, 1) +
qutip.entropy_conditional(bd, 1)))
def test_EntropyConditional():
"Conditional entropy"
# test_ S(A,B|C,D)<=S(A|C)+S(B|D)
rhos = [rand_dm(16, dims=[[2, 2, 2, 2], [2, 2, 2, 2]], pure=True)
for k in range(20)]
for ABCD in rhos:
AC = ptrace(ABCD, [0, 2])
BD = ptrace(ABCD, [1, 3])
assert_equal(entropy_conditional(ABCD, [2, 3]) <= (
entropy_conditional(AC, 1) + entropy_conditional(BD, 1)), True)
# test_ S(A|B,C)<=S(A|B)
rhos = [rand_dm(8, dims=[[2, 2, 2], [2, 2, 2]], pure=True)
for k in range(20)]
for ABC in rhos:
AB = ptrace(ABC, [0, 1])
assert_equal(entropy_conditional(
ABC, [1, 2]) <= entropy_conditional(AB, 1), True)
def test_inequality_3_qubits(self):
# S(A | B,C) <= S(A|B)
full = qutip.rand_dm(8, dims=[[2] * 3] * 2, pure=True)
ab = full.ptrace([0, 1])
assert (qutip.entropy_conditional(full, [1, 2]) <=
qutip.entropy_conditional(ab, 1))