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Physical Review B

Local measurement of the entanglement between two quantum-dot qubits

Liu Jin, Zhaotan Jiang, Bin Shao

Published Mar 30, 2009• 8 citations
Publisher

Abstract

Using the modified rate equation the local measurement of the entanglement between two quantum-dot qubits, with two isolated quantum-point-contact detectors, is investigated. It is shown that the measurement process will induce the decaying of the two-qubit entanglement, as well as the electron-occupation probabilities. Furthermore, we find an effective scheme to measure the two-qubit entanglement based on the local measurement. It is demonstrated that the entanglement between the two qubits coupled by the strong Coulomb interaction can be fully extracted according to the time-dependent variation rate of the detector current.

DOI
10.1103/physrevb.79.115323

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Using the modified rate equation the local measurement of the entanglement between two quantum-dot qubits, with two isolated quantum-point-contact detectors, is investigated. It is shown that the measurement process will induce the decaying of the two-qubit entanglement, as well as the electron-occupation probabilities. Furthermore, we find an effective scheme to measure the two-qubit entanglement based on the local measurement. It is demonstrated that the entanglement between the two qubits coupled by the strong Coulomb interaction can be fully extracted according to the time-dependent variation rate of the detector current.
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 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.
In this paper we propose a novel measurement scheme, based on a double quantum-dot detector, for reading out the qubit information sensed by the detector as a variation of the interdot coupling. By investigating the detector in the static qubit case, we find a sensitive qubit-detector response region determined by the detector geometry. Then we study quantum measurement of the information stored in a dynamic qubit. It is verified that whether the detector can perform well is closely dependent on the ratio of the right dot-lead coupling to interdot coupling in the detector, while the interdot Coulomb interaction only plays a trivial role. Furthermore, it is shown that the dephasing time of the qubit is strongly influenced by the difference between the interdot couplings of the detector corresponding to two qubit states. This work provides some helpful instructions on how to devise an effective qubit detector.
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.
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.
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.