def setsympaulibasis(self,rho=None):
"""
Set symmetric Pauli operator basis
Determine internal symmetries of a state to provide a basis spanning the minimal subspace containing the optimal witness
rho : array_like
An array_like object representing a density matrix of the given system.
As an example use the basis symmetric with respect to the GHZ and W state to calculate the genuine multiparticle negativity of the GHZ state
>>> from gmntools import gmn
>>> ghz = [[.5,0,0,0,0,0,0,.5],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[.5,0,0,0,0,0,0,.5]]
>>> w = [[0,0,0,0,0,0,0,0],[0,1./3.,1./3.,0,1./3.,0,0,0],[0,1./3.,1./3.,0,1./3.,0,0,0],[0,0,0,0,0,0,0,0],[0,1./3.,1./3.,0,1./3.,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]]
>>> gmntool = gmn([2,2,2],ghz)
Determine a basis symmetric with respect to the current density matrix
>>> gmntool.setsympaulibasis()
>>> gmntool.gmn()
0.4999999983690673
Change to a basis symmetric with respect to the W state. No witness detecting genuine multiparticle entangelement is found within this subspace
>>> gmntool.setsympaulibasis(w)
>>> gmntool.gmn()
-1.7734501447089677e-09
"""
if not all([2==i for i in self.__dimsubs]):
raise TypeError("Memberfuction availible in qubit systems only.")
if not rho:
if not self.__rho:
raise TypeError("Set density matrix before calling Memberfunction or provide density matrix as argument.")
else:
self.setoperatorbasis(pauli(self.__nsys).symbasis(self.__rho.matrix))
else:
self.setoperatorbasis(pauli(self.__nsys).symbasis(rho))
def setpaulibasis(self):
"""
Set Pauli operator basis
Use a operator basis consisting of tensor products of Pauli operators
Try to find the optimal witness within the operator subspace spanned by pauli operators X,Y,Z and qubit identity matrices (1): 111, XXZ, XZX, ZXX, ZZZ
>>> from gmntools import gmn
>>> ghz = [[.5,0,0,0,0,0,0,.5],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[.5,0,0,0,0,0,0,.5]]
>>> gmntool = gmn([2,2,2],ghz)
Use a basis of tensor products of Pauli matrices as basis
>>> gmntool.setpaulibasis()
>>> gmntool.gmn()
0.49999999836906783
Reset to the default operator basis
>>> gmntool.setoperatorbasis()
>>> gmntool.gmn()
0.499999998369068
"""
if not all([2==i for i in self.__dimsubs]):
raise TypeError("Memberfuction availible in qubit systems only.")
self.setoperatorbasis(pauli(self.__nsys).basis())
