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((E1−E2)/)
2 (ρ11 − ρ22) + (ρ12 + ρ21), where the normalization condition 1 − ρ00 = ρ11 + ρ22
is used, becomes EDQD = E1+E2
2 (1 − ρ00) + (ρ12 + ρ21). When there is no electrons in
the dots, ρ00 = 1, the energy of the dots is simply zero. And the choice of E1 = E2 = 0
will cause that the energy of the dots when there is one electron in double dots, ρ11 = 1
or ρ22 = 1 is also 0. In the case where there is no charge leakage this choice of energy
reference is ok. However for the charge qubit being an open system, charge leakage shall be
considered and the choice of energy reference would matter if we look at the time evolution
of the energy of the dots. Otherwise, this choice of energy reference matters nothing as
long as the total energy configuration, the relations between the dot energy levels and the
chemical potentials in the electron reservoirs, remains the same. We can see identical time
evolutions of the density matrix at the energy references E = 0 and E = 0 with the relations
between E and μ1,2 fixed. But the dot energy EDQD given above is of course influenced by
the energy reference.
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