def entropy_conditional(rho, selB, base=e, sparse=False):
"""
Calculates the conditional entropy :math:`S(A|B)=S(A,B)-S(B)`
of a selected density matrix component.
Parameters
----------
rho : qobj
Density matrix of composite object
selB : int/list
Selected components for density matrix B
base : {e,2}
Base of logarithm.
sparse : {False,True}
Use sparse eigensolver.
Returns
-------
ent_cond : float
Value of conditional entropy
"""
if rho.type != 'oper':
raise TypeError("Input must be density matrix.")
if isinstance(selB, int):
selB = [selB]
B = ptrace(rho, selB)
out = (entropy_vn(rho, base, sparse=sparse) -
entropy_vn(B, base, sparse=sparse))
return out
def entropy_conditional(rho, selB, base=e, sparse=False):
"""
Calculates the conditional entropy :math:`S(A|B)=S(A,B)-S(B)`
of a slected density matrix component.
Parameters
----------
rho : qobj
Density matrix of composite object
selB : int/list
Selected components for density matrix B
base : {e,2}
Base of logarithm.
sparse : {False,True}
Use sparse eigensolver.
Returns
-------
ent_cond : float
Value of conditional entropy
"""
if rho.type != 'oper':
raise TypeError("Input must be density matrix.")
if isinstance(selB, int):
selB = [selB]
B = ptrace(rho, selB)
out = (entropy_vn(rho, base, sparse=sparse) -
entropy_vn(B, base, sparse=sparse))
return out
def entropy_mutual(rho, selA, selB, base=e, sparse=False):
"""
Calculates the mutual information S(A:B) between selection
components of a system density matrix.
Parameters
----------
rho : qobj
Density matrix for composite quantum systems
selA : int/list
`int` or `list` of first selected density matrix components.
selB : int/list
`int` or `list` of second selected density matrix components.
base : {e,2}
Base of logarithm.
sparse : {False,True}
Use sparse eigensolver.
Returns
-------
ent_mut : float
Mutual information between selected components.
"""
if isinstance(selA, int):
selA = [selA]
if isinstance(selB, int):
selB = [selB]
if rho.type != "oper":
raise TypeError("Input must be a density matrix.")
if (len(selA) + len(selB)) != len(rho.dims[0]):
raise TypeError("Number of selected components must match " + "total number.")
rhoA = ptrace(rho, selA)
rhoB = ptrace(rho, selB)
out = (
entropy_vn(rhoA, base, sparse=sparse)
+ entropy_vn(rhoB, base, sparse=sparse)
- entropy_vn(rho, base, sparse=sparse)
)
return out
def entropy_mutual(rho, selA, selB, base=e, sparse=False):
"""
Calculates the mutual information S(A:B) between selection
components of a system density matrix.
Parameters
----------
rho : qobj
Density matrix for composite quantum systems
selA : int/list
`int` or `list` of first selected density matrix components.
selB : int/list
`int` or `list` of second selected density matrix components.
base : {e,2}
Base of logarithm.
sparse : {False,True}
Use sparse eigensolver.
Returns
-------
ent_mut : float
Mutual information between selected components.
"""
if isinstance(selA, int):
selA = [selA]
if isinstance(selB, int):
selB = [selB]
if rho.type != 'oper':
raise TypeError("Input must be a density matrix.")
if (len(selA) + len(selB)) != len(rho.dims[0]):
raise TypeError("Number of selected components must match " +
"total number.")
rhoA = ptrace(rho, selA)
rhoB = ptrace(rho, selB)
out = (entropy_vn(rhoA, base, sparse=sparse) +
entropy_vn(rhoB, base, sparse=sparse) -
entropy_vn(rho, base, sparse=sparse))
return out
def test_N_level_system(self):
"""
Test for circuit with N-level system.
"""
mat3 = rand_dm(3, density=1.)
def controlled_mat3(arg_value):
"""
A qubit control an operator acting on a 3 level system
"""
control_value = arg_value
dim = mat3.dims[0][0]
return (tensor(fock_dm(2, control_value), mat3) +
tensor(fock_dm(2, 1 - control_value), identity(dim)))
qc = QubitCircuit(2, dims=[3, 2])
qc.user_gates = {"CTRLMAT3": controlled_mat3}
qc.add_gate("CTRLMAT3", targets=[1, 0], arg_value=1)
props = qc.propagators()
assert_allclose(mat3, ptrace(props[0], 0) - 1)