def main1():
print('--------------------main1')
np.random.seed(123)
dm = DenMat(8, (2, 2, 2))
exact_evas = np.array([.1, .3, .3, .1, .2, .1, .6, .7])
exact_evas /= np.sum(exact_evas)
print('evas of dm\n', np.sort(exact_evas))
dm.set_arr_to_rand_den_mat(exact_evas)
pert = DenMatPertTheory.new_with_separable_dm0(dm, verbose=True)
# print('evas of dm to 2nd order (after 1 step)\n',
# np.sort(pert.evas_of_dm_to_2nd_order),
# 'sum=', np.sum(pert.evas_of_dm_to_2nd_order))
# print('evas of dm\n', np.sort(evas))
# print('evas_of_dm0\n', pert.dm0_eigen_sys[0])
#
# print('diag of del_dm in sbasis\n',
# np.diag(pert.del_dm_in_sbasis.arr.real))
# print('del_dm\n', pert.del_dm)
# dm0 = pert.get_dm0()
# print('dm0\n', dm0)
num_steps = 40
# print('evas_of_dm\n', evas)
main_test(dm, exact_evas, pert, num_steps)
def main():
num_qbits = 5
num_up = 2
dm = DenMat(1 << num_qbits, tuple([2]*num_qbits))
st = SymNupState(num_up, num_qbits)
st_vec = st.get_st_vec()
dm.set_arr_from_st_vec(st_vec)
ecase = PureStEnt(dm, 'eigen')
pf = ecase.get_entang_profile()
# print(',,...', pf)
ecase.print_entang_profiles([pf, pf], dm.row_shape)
def main2():
print('--------------------main2')
np.random.seed(123)
dm1 = DenMat(3, (3,))
evas1 = np.array([.1, .1, .4])
evas1 /= np.sum(evas1)
dm1.set_arr_to_rand_den_mat(evas1)
# print('dm1\n', dm1)
dm2 = DenMat(2, (2,))
evas2 = np.array([.8, .3])
evas2 /= np.sum(evas2)
dm2.set_arr_to_rand_den_mat(evas2)
# print('dm2\n', dm2)
dm = DenMat.get_kron_prod_of_den_mats([dm1, dm2])
const = 0
# const = 1
dm.add_const_to_diag_of_arr(const)
dm.normalize_diag_of_arr()
print('kron evas\n', np.sort(ut.kron_prod([evas1, evas2])))
exact_evas = np.linalg.eigvalsh(dm.arr)
print('evas_of_dm\n', exact_evas)
pert = DenMatPertTheory.new_with_separable_dm0(dm, verbose=True)
# print('evas of dm to 2nd order (after 1 step)\n',
# np.sort(pert.evas_of_dm_to_2nd_order),
# 'sum=', np.sum(pert.evas_of_dm_to_2nd_order))
num_steps = 10
main_test(dm, exact_evas, pert, num_steps)
def main3():
print('--------------------main3')
num_qbits = 4
num_up = 2
dm = DenMat(1 << num_qbits, tuple([2]*num_qbits))
st = SymNupState(num_up, num_qbits)
st_vec = st.get_st_vec()
dm.set_arr_from_st_vec(st_vec)
# dm.depurify(.1)
exact_evas = np.linalg.eigvalsh(dm.arr)
print('evas_of_dm\n', exact_evas, 'sum=', np.sum(exact_evas))
pert = DenMatPertTheory.new_with_separable_dm0(dm, verbose=True)
num_steps = 80
main_test(dm, exact_evas, pert, num_steps)
def do_bstrap_with_separable_dm0(dm, num_steps=1, verbose=False):
"""
This method returns the same thing as the method (found in its
parent class) DenMatPertTheory.do_bstrap( ). However, their names
differ by a '_with_separable_dm0' at the end and their inputs are
different. This one takes as input a density matrix dm and
calculates dm0_eigen_sys and del_dm from that, assuming that dm0 is
the Kronecker product of the marginals of dm.
Parameters
----------
dm : DenMat
num_steps : int
verbose : bool
Returns
-------
tuple[np.ndaray, np.ndarray]
"""
if dm.marginals is None:
dm.set_marginals()
esys = dm.get_eigen_sys_of_marginals()
dm0_eigen_sys = (ut.kron_prod(esys[0]),
ut.kron_prod(esys[1]))
arr = ut.kron_prod([marg.arr for marg in dm.marginals])
dm0 = DenMat(dm.num_rows, dm.row_shape, arr)
return DenMatPertTheory.do_bstrap(
dm0_eigen_sys, dm-dm0, num_steps, verbose)
def get_den_mat_with_bound_entang(p):
"""
This method returns a DenMat with num_rows = 8 and row_shape = (2,
4) that is known to have bound entanglement.
https://arxiv.org/abs/quant-ph/9703004
Parameters
----------
p : float
a probability, 0 < p < 1
Returns
-------
DenMat
"""
num_rows = 8
row_shape = (2, 4)
a = (1 + p) / 2
b = np.sqrt(1 - p**2) / 2
arr1 = np.array([[p, 0, 0, 0, 0, p, 0, 0], [0, p, 0, 0, 0, 0, p, 0],
[0, 0, p, 0, 0, 0, 0, p], [0, 0, 0, p, 0, 0, 0, 0],
[0, 0, 0, 0, a, 0, 0, b], [p, 0, 0, 0, 0, p, 0, 0],
[0, p, 0, 0, 0, 0, p, 0], [0, 0, p, 0, b, 0, 0, a]])
return DenMat(num_rows, row_shape, arr1 / np.trace(arr1))
def get_bell_basis_diag_dm(fid, prob_dict=None):
"""
This method returns a DenMat which is constructed as a linear
combination, with coefficients prob_dict, of the Bell basis state
projection operators. So the den matrix returned is diagonal in the
Bell basis.
If prob_dict is not None, use it and ignore value of fid. If
prob_dict is None, use prob_dict for an "isotropic" Werner state
with fidelity fid. That is, prob_dict[ "==+"]=fid, prob_dict[x]=(
1-fid)/3 for all x other than '==+"
Parameters
----------
fid : float
fidelity.
prob_dict : dict[str, float]|None
Returns
-------
DenMat
"""
if prob_dict:
assert ut.is_prob_dist(np.array(list(prob_dict.values())))
assert set(prob_dict.keys()) == TwoQubitState.bell_key_set()
else:
assert 0 <= fid <= 1
prob_dict = {}
for key in TwoQubitState.bell_key_set():
if key == '==+':
prob_dict[key] = fid
else:
prob_dict[key] = (1 - fid) / 3
dm = DenMat(4, (2, 2))
dm.set_arr_to_zero()
for key in prob_dict.keys():
st_vec = TwoQubitState.get_bell_basis_st_vec(key)
dm.arr += np.outer(st_vec, np.conj(st_vec)) * prob_dict[key]
return dm
def main():
print('4 Bell Basis states**********************')
for bits_are_equal in [True, False]:
for mid_sign in ['+', '-']:
st_vec = OtherStates.get_bell_basis_st_vec(bits_are_equal, mid_sign)
dm = DenMat(4, (2, 2))
dm.set_arr_from_st_vec(st_vec)
ecase = PureStEnt(dm)
pf = ecase.get_entang_profile()
print('----------bits_are_equal=', bits_are_equal,
', mid_sign=', mid_sign)
print("st_vec=\n", st_vec)
ecase.print_entang_profiles([pf], dm.row_shape)
print('bound entang state **********************')
dm_bd = OtherStates.get_den_mat_with_bound_entang(.5)
num_hidden_states = 5
num_ab_steps = 30
ecase = SquashedEnt(dm_bd, num_hidden_states, num_ab_steps,
verbose=True)
pf = ecase.get_entang_profile()
ecase.print_entang_profiles([pf], dm_bd.row_shape)
def check_max_entang_st(st):
"""
This method checks that the object st of class MaxEntangState does
indeed carry maximal entanglement. The entanglement is calculated 3
different ways (von Neumann entropy of 2 partial traces of density
matrix, and from known value) and the 3 values are checked to agree.
Parameters
----------
st : MaxEntangState
Returns
-------
None
"""
dm = DenMat(st.num_rows, st.row_shape)
st_vec = st.get_st_vec()
dm.set_arr_from_st_vec(st_vec)
ent1 = dm.get_partial_tr(set(st.y_axes)).get_entropy()
ent2 = dm.get_partial_tr(set(st.x_axes)).get_entropy()
ent3 = np.log(st.num_vals_min)
assert abs(ent1 - ent2) < 1e-6 and abs(ent1 - ent3) < 1e-6, \
str(ent1) + ', ' + str(ent2) + ', ' + str(ent3)
def get_dm0(self):
"""
This method returns the unperturbed density matrix dm0. We define
this method so as to avoid storing dm0.
Returns
-------
DenMat
"""
evas = self.dm0_eigen_sys[0]
evec_cols = self.dm0_eigen_sys[1]
arr = ut.fun_of_herm_arr_from_eigen_sys(lambda x: x, evas, evec_cols)
num_rows = self.del_dm.num_rows
row_shape = self.del_dm.row_shape
return DenMat(num_rows, row_shape, arr)
def get_time_reversed_dm(dm):
"""
This method returns a DenMat which is the time reversed version of a
DenMat dm for 2 qubits.
Parameters
----------
dm : DenMat
Returns
-------
DenMat
"""
assert dm.num_rows == 4
sigy = np.array([[0, -1j], [1j, 0]])
dm_sigyy = DenMat(4, (2, 2), arr=ut.kron_prod([sigy, sigy]))
return dm_sigyy * dm.conj() * dm_sigyy
def new_with_separable_dm0(dm, verbose=False):
"""
This method returns a DenMatPertTheory built from a density matrix
dm, assuming that dm0 is the Kronecker product of the marginals of dm.
Parameters
----------
dm : DenMat
verbose : bool
Returns
-------
DenMatPertTheory
"""
if dm.marginals is None:
dm.set_marginals()
esys = dm.get_eigen_sys_of_marginals()
dm0_eigen_sys = (ut.kron_prod(esys[0]), ut.kron_prod(esys[1]))
arr = ut.kron_prod([marg.arr for marg in dm.marginals])
dm0 = DenMat(dm.num_rows, dm.row_shape, arr)
return DenMatPertTheory(dm0_eigen_sys, dm - dm0, verbose)
def main1():
print('4 Bell Basis states**********************')
for key in TwoQubitState.bell_key_set():
st_vec = TwoQubitState.get_bell_basis_st_vec(key)
dm = DenMat(4, (2, 2))
dm.set_arr_from_st_vec(st_vec)
ecase = PureStEnt(dm)
pf = ecase.get_entang_profile()
print('----------key:', key)
print("st_vec=\n", st_vec)
ecase.print_entang_profiles([pf], dm.row_shape)
print("*******************************")
dm1 = TwoQubitState.get_bell_basis_diag_dm(fid=.7)
# print('arr=\n', dm1.arr)
np.random.seed(123)
dm2 = DenMat(4, (2, 2))
dm2.set_arr_to_rand_den_mat(np.array([.1, .2, .3, .4]))
dm3 = DenMat(4, (2, 2))
dm3.set_arr_to_rand_den_mat(np.array([.1, .1, .1, .7]))
for dm in [dm1, dm2, dm3]:
print("----------new dm")
print("formation_entang=",
TwoQubitState.get_known_formation_entang(dm))
