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_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
