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arXiv:cond-mat/0310293 · Journal of Physics Condensed Matter

Measurement of two-qubit states with quantum point contacts coupled by a quantum dot

Tetsufumi Tanamoto, Xuedong Hu

Published Oct 14, 2005• 6 citations
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Abstract

We solve the master equations of two charge qubits measured by two serially coupled quantum point contacts (QPCs). We describe two-qubit dynamics by comparing entangled states with product states, and show that the QPC current can be used for reading out results of quantum calculations and providing evidences of two-qubit entanglement. We also calculate the concurrence of the two qubits as a function of dephasing rate that originates from the measurement. We conclude that coupled charge qubits can be effectively detected by a QPC-based detector.

DOI
10.1088/0953-8984/17/43/009

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We solve the master equations of two charge qubits measured by two serially coupled quantum point contacts (QPCs). We describe two-qubit dynamics by comparing entangled states with product states, and show that the QPC current can be used for reading out results of quantum calculations and providing evidences of two-qubit entanglement. We also calculate the concurrence of the two qubits as a function of dephasing rate that originates from the measurement. We conclude that coupled charge qubits can be effectively detected by a QPC-based detector.
We present the measurement of a hybrid double-dot qubit using a quantum point contact (QPC). To study the dynamics, we derive the rate equations of the entire system. Numerical results show that QPC current can directly reflect the evolution of the qubit. By adjusting Coulomb interaction, energy mismatch, and QPC tunneling rate, the efficiency and dephasing time can be improved. In addition, the initial state with a hybrid triplet state is superior to that with the purely triplet states on the efficiency. Moreover, the decoherence time is estimated on the magnitude of a microsecond, long enough to implement quantum operations.
We study the dynamics of two electron spins in coupled quantum dots (CQDs) monitored by a quantum point contact (QPC) detector. Their quantum state can be measured by embedding the QPC in an LC circuit. We derive the Bloch-type rate equations of the reduced density matrix for CQDs. Special attention is paid to the numerical results for the weak measurement condintion under a strong Coulomb interaction. It is shown that the evolution of QPC current always follows that of electron occupation in the right dot. In addition, we find that the output voltage of the circuit can reflect the evolution of QPC current when the circuit and QPC are approximately equal in frequency. In particular, the wave shape of the output voltage can be improved by adjusting the circuit resonance frequency and bandwidth.
Using the method developed by Gurvitz of solving Schrdinger equations and the numerical calculation, we investigate the oscillation and the entanglement of the two opposite-spin electrons in coupled quantum dots, and show how to read out the entanglement by quantum point-contact detector. The results show that the two electrons start to entangle due to Coulomb interaction, and then they move together with Coulomb interaction augmenting, similar to the oscillation of an electron in a qibit. In this case, we locate a quantum point contact detector near one of the quantum dots, and the entanglement information can be obtained by changing the current.
We propose a direct measurement scheme to read out the geometric phase of a coupled double quantum dot system via a quantum point contact(QPC) device. An effective expression of the geometric phase has been derived, which relates the geometric phase of the double quantum dot qubit to the current through QPC device. All the parameters in our expression are measurable or tunable in experiment. Moreover, since the measurement process affects the state of the qubit slightly, the geometric phase can be protected. The feasibility of the scheme has been analyzed. Further, as an example, we simulate the geometrical phase of a qubit when the QPC device is replaced by a single electron transistor(SET).
Entanglement between a particle and a detector is known to be inherent in the measurement process. Gurvitz recently analyzed the coupling of an electron in a double dot (DD) to a quantum point contact (QPC) detector. In this paper we examine the dynamics of entanglement that result between the DD and QPC. The rate of entanglement is optimized as a function of coupling when the electron is initially in one of the dots. It decreases asymptotically towards zero with increased coupling. The opposite behavior is observed when the DD is initially in a superposition: the rate of entanglement increases unboundedly as the coupling is increased. The possibility that there are conditions for which measurement occurs versus entanglement is considered.