def WORMHOLE(tL, tR, beta, g, m, n):
#H = qt.rand_herm(2**n)
#H = rand_scrambler(n)
global q, H, HL, HV, TFD, LBACK, TFD2, TFD3
global TFD4, LFORWARD, TFD5, V
#H = 1j*qt.Qobj(scipy.linalg.logm(U.full()))
COUPLING = (1j*g*V).expm()
TFD6 = COUPLING*TFD5
TFD7 = RFORWARD*TFD6
FIN = TFD7
o = m+n+1
#print("%d should be %f" % (o, 2*np.log(2)))
if False:
for i in range(len(FIN.dims[0])):
if i != 0:
if i == o:
print("*")
f = FIN.ptrace((0, i))
e = qt.entropy_mutual(f, 0, 1)
print ("subs 0 and %d: e = %.6f" % (i,e))
print()
fin = FIN.ptrace((0, o))
e = qt.entropy_mutual(fin, 0, 1)
should_be = 2*np.log(2)
return "e: %f | %f" % (e, should_be)
def calculate_mutual_information(self, loud=True):
self.should_be = 2 * np.log(2)
self.FIN = self.FINAL.ptrace(
list(range(self.m)) +
list(range(2 * self.m + self.n, 3 * self.m + self.n)))
self.mutual_info = qt.entropy_mutual(self.FIN, list(range(self.m)),
list(range(self.m, 2 * self.m)))
if loud:
for i in range(self.m, self.ntotal_qubits):
fin = self.FINAL.ptrace(list(range(self.m)) + [i])
mut_inf = qt.entropy_mutual(fin, list(range(self.m)), [self.m])
print("%s\te between ref and qubit %d: %.5f" %
("*" if i == self.output_index else "", i, mut_inf))
def test_EntropyMutual():
"Mutual information"
# verify mutual information = S(A)+S(B) for pure state
rhos = [rand_dm(25, dims=[[5, 5], [5, 5]], pure=True) for k in range(10)]
for r in rhos:
assert_equal(abs(entropy_mutual(r, [0], [1]) - (
entropy_vn(ptrace(r, 0)) + entropy_vn(ptrace(r, 1)))) < 1e-13,
True)
# check component selection
rhos = [rand_dm(8, dims=[[2, 2, 2], [2, 2, 2]], pure=True)
for k in range(10)]
for r in rhos:
assert_equal(abs(entropy_mutual(r, [0, 2], [1]) - (entropy_vn(
ptrace(r, [0, 2])) + entropy_vn(ptrace(r, 1)))) < 1e-13, True)
def test_EntropyMutual():
"Entropy: Mutual information"
# verify mutual information = S(A)+S(B) for pure state
rhos = [rand_dm(25, dims=[[5, 5], [5, 5]], pure=True) for k in range(10)]
for r in rhos:
assert_equal(
abs(
entropy_mutual(r, [0], [1]) -
(entropy_vn(ptrace(r, 0)) + entropy_vn(ptrace(r, 1)))) < 1e-13,
True)
# check component selection
rhos = [
rand_dm(8, dims=[[2, 2, 2], [2, 2, 2]], pure=True) for k in range(10)
]
for r in rhos:
assert_equal(
abs(
entropy_mutual(r, [0, 2], [1]) -
(entropy_vn(ptrace(r, [0, 2])) + entropy_vn(ptrace(r, 1)))) <
1e-13, True)
def test_component_selection(self):
dm = qutip.rand_dm(8, dims=[[2, 2, 2], [2, 2, 2]], pure=True)
expect = (qutip.entropy_vn(dm.ptrace([0, 2])) +
qutip.entropy_vn(dm.ptrace(1)))
assert abs(qutip.entropy_mutual(dm, [0, 2], [1]) - expect) < 1e-13
def test_pure_state_additive(self):
# Verify mutual information = S(A) + S(B) for pure states.
dm = qutip.rand_dm(25, dims=[[5, 5], [5, 5]], pure=True)
expect = (qutip.entropy_vn(dm.ptrace(0)) +
qutip.entropy_vn(dm.ptrace(1)))
assert abs(qutip.entropy_mutual(dm, [0], [1]) - expect) < 1e-13
