def fidelity(statevec, dm, u_dm, ustatevec=np.array([0, 0])):
'''
returns the fidelity (and its uncertainty) of the measured density
matrix with a given state vector.
'''
f = error.Formula()
beta, a, x, b, alpha = sympy.symbols('beta,a,x,b,alpha')
v = Matrix([alpha, beta])
rho = Matrix([[x, a + 1j * b], [a - 1j * b, 1 - x]])
f.formula = (v.conjugate().transpose() * rho * v)[0]
f.values[alpha] = statevec[0]
f.values[beta] = statevec[1]
f.values[a] = float(np.real(dm[0, 1]))
f.values[x] = float(dm[0, 0])
f.values[b] = float(np.imag(dm[0, 1]))
f.uncertainties[alpha] = ustatevec[0]
f.uncertainties[beta] = ustatevec[1]
f.uncertainties[x] = u_dm[0, 0]
f.uncertainties[a] = float(np.real(u_dm[0, 1]))
f.uncertainties[b] = float(np.imag(u_dm[0, 1]))
_fid, _ufid = f.num_eval()
fid = float(_fid.as_real_imag()[0])
ufid = float(_ufid.as_real_imag()[0])
return (fid, ufid)
def fidelity(statevec, dm, u_dm, ustatevec=np.array([0,0])):
'''
returns the fidelity (and its uncertainty) of the measured density
matrix with a given state vector.
'''
f = error.Formula()
beta,a,x,b,alpha = sympy.symbols('beta,a,x,b,alpha')
v = Matrix([alpha, beta])
rho = Matrix([[x,a+1j*b],[a-1j*b, 1-x]])
f.formula = (v.conjugate().transpose() * rho * v)[0]
f.values[alpha] = statevec[0]
f.values[beta] = statevec[1]
f.values[a]=float(np.real(dm[0,1]))
f.values[x]=float(dm[0,0])
f.values[b]=float(np.imag(dm[0,1]))
f.uncertainties[alpha]=ustatevec[0]
f.uncertainties[beta]=ustatevec[1]
f.uncertainties[x]=u_dm[0,0]
f.uncertainties[a]=float(np.real(u_dm[0,1]))
f.uncertainties[b]=float(np.imag(u_dm[0,1]))
_fid,_ufid = f.num_eval()
fid = float(_fid.as_real_imag()[0])
ufid = float(_ufid.as_real_imag()[0])
return (fid,ufid)
def as_density_matrix(self):
"""
NOT USED ANYMORE (but works fine)
Represent this pure state as density matrix.
"""
coeffs = self.get_coefficients_as_general_state()
matrix = Matrix(coeffs)
matrix = matrix * matrix.conjugate().transpose()
coeff_comm = self.coeff_comm
matrix = matrix * coeff_comm * coeff_comm
return matrix