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Acta Physica Sinica

Measurement of entanglement in coupled dots

Haixia Wang, Yin Wen, Wang Fang-Wei

Published Jan 1, 2010• 3 citations
Publisher

Abstract

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.

DOI
10.7498/aps.59.5241

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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.
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.
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.
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 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.
Addressing the feasibility of quantum communication with electrons we consider entangled spin states of electrons in a double-dot which is weakly coupled to leads. We show that the entanglement of two electrons in the double-dot can be detected in mesoscopic transport and noise measurements. In the Coulomb blockade and cotunneling regime the singlet and triplet states lead to phase-coherent current and noise contributions of opposite signs and to Aharonov-Bohm and Berry phase oscillations. These oscillations are a genuine two-particle effect and provide a direct measure of nonlocality in entangled states. We show that the ratio of zero-frequency noise to current is equal to the electron charge.