# Photon Enhanced Interaction and Entanglement in Semiconductor Position-Based Qubits
## 3 Position-Based Semiconductor Qubits in the Frame of Semiconductor Photon Communication
### Simulation Results  
The time evolution of the probabilities of different quantum states, as obtained from solving (15), is depicted in Figure 4. The probability of the states \(\ket{0_{g}}\) and \(\ket{0_{e}}\) is visualized in Figure 4a. The probabilities of the localized states \(\ket{0}\) are, as expected, anti-correlated. Similarly, the probabilities \(\ket{1_{g}}\) and \(\ket{1_{e}}\) are also anti-correlated, as shown in Figure 4b. Therefore, the evolution of quantum states in terms of ground \(\ket{g}\) and excited \(\ket{e}\) energies exhibits an anti-correlation. Moreover, in Figure 4c one can see that the anti-correlation occurs also in the probabilities of the two localized states \(\ket{0_{g}}\) and \(\ket{1_{g}}\), of a quantum particle of the same ground level, \(\ket{g}\), i.e., this is a positional anti-correlation. The same positional anti-correlation occurs between the two localized states, \(\ket{0_{e}}\) and \(\ket{1_{e}}\), but now of the same excited energy level, as depicted in Figure 4d.  
Figure 3: Potential energy profile as a piecewise approximation of a double-well with four energy-levels. This function is extracted from COMSOL electrostatic simulations, assuming carrier freezout operation. The number of bound states in the double well depends on a particular voltage configuration applied at the gates. Therefore, it is possible to electrostatically control the energy gaps between the different energy levels. In addition, the energy levels of a given potential energy double well determine the allowed energies of photons that are possible to emtite and absorb during the quantum operation between communicating qubits.  
Finally, to conclude the analysis of the system of a single qubit, an example of a typical quantum path following the time evolution of (15) is presented in Figure 5, where a photon is absorpted during a transition from a localized ground state \(\ket{g}\) to a localized excited state \(\ket{e}\), while a photon is emitted during a transition from the state \(\ket{e}\) to the state \(\ket{g}\). After obtaining the expressions for the evolution of various amplitude probabilities from (17), we follow the numerical approach of [23] to simulate the quantum path.  
Figure 4: **(a)** Evolution of the probability of the states \(\ket{0_{g}}\) and \(\ket{0_{e}}\). These states correspond to the same position (localized state \(\ket{0}\)) but different energy levels (ground state \(\ket{g}\)) and excited state \(\ket{e}\)). It is observed that they are anti-correlated. **(b)** Time Evolution of the probability of the states \(\ket{1_{g}}\) and \(\ket{1_{e}}\). Similarly, these states correspond to the same position (in this case the localized state \(\ket{1}\)). Energy anti-correlation is also observed in this case. **(c)** The time evolution of the probability of the states \(\ket{0_{g}}\) and \(\ket{1_{g}}\). These states correspond to the same ground energy level (energy state \(\ket{g}\)) but different position (localized states \(\ket{0}\) and \(\ket{1}\)). Therefore, they are anti-correlated. **(d)** Time evolution of the probability of the states \(\ket{0_{e}}\) and \(\ket{1_{e}}\). These states correspond to the same excited energy level (in this case energy state \(\ket{e}\)) but different position (localized states \(\ket{0}\) and \(\ket{1}\)). They are also anti-correlated.