Parity meter for charge qubits: An efficient quantum entangler

We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact. Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)]. Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter. Two applications of the parity meter are discussed: the measurement of Bell’s inequality in charge qubits and the realization of a controlled-NOT gate.

Figure 1

Parity meter setup. In (a), two DQD’s are shown with a QPC in between them. By measuring the current through the QPC, we are able to determine the parity class of the two-qubit state formed by a single electron in each DQD qubit. In (b), a capacitive model is illustrated for the setup considered in (a). The two gray boxes in the middle correspond to the dipole across the QPC.

Figure 2

(Color online) Upper part: Top view of QPC in the parity meter setup. In the odd parity class, where $(Q_L,Q_R)$ is $(1,-1)$ or $(-1,1)$, no dipole is generated across the QPC and it is nicely symmetric. In the even parity class, where $(Q_L,Q_R)$ is $(1,1)$ or $(-1,-1)$, the situation is different. There, a dipole is generated across the QPC by the particular position of the electrons in the quantum dots. The dipole shifts the saddle point to the right (left) depending on the direction of the polarization of the dipole, but for both polarizations the shift is to higher energies. Note that the QPC in this figure is rotated by ${90}^{\circ }$ with respect to the QPC in Fig. 1. Lower part: Illustration of the saddle point potential for the two configurations.

Figure 3

Bell inequality setup. In order to be able to do a measurement of a violation of a Bell inequality, we use a QPC as a parity meter between two qubits to create a Bell state. The two outer detectors are then used to projectively measure charge in the ${\sigma }_z$ basis of each qubit.

Figure 4

CNOT gate setup. This setup contains three qubits and two parity meters, i.e., QPC’s, in between them. The qubits are the control qubit $\left(\mathrm{C}\mathrm{qubit}\right)$, the ancilla qubit $\left(\mathrm{A}\mathrm{qubit}\right)$, and the target qubit $\left(\mathrm{T}\mathrm{qubit}\right)$. An additional projective measurement device is attached to the $\mathrm{A}\mathrm{qubit}$.