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arXiv:0710.4120 · Physical Review B

Entanglement generation via a completely mixed nuclear spin bath

H. Christ, J. I. Cirac, G. Giedke

Published Sep 12, 2008• 18 citations
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Abstract

We show that qubits coupled sequentially to a mesoscopic static completely mixed spin bath via the Heisenberg interaction can become highly entangled. Straightforward protocols for the generation of multipartite entangled Greenberger-Horne-Zeilinger (GHZ) states are presented. We show the feasibility of an experimental realization in a quantum dot by the hyperfine interaction of an electron with the nuclear spins.

DOI
10.1103/physrevb.78.125314

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We show that qubits coupled sequentially to a mesoscopic static completely mixed spin bath via the Heisenberg interaction can become highly entangled. Straightforward protocols for the generation of multipartite entangled Greenberger-Horne-Zeilinger (GHZ) states are presented. We show the feasibility of an experimental realization in a quantum dot by the hyperfine interaction of an electron with the nuclear spins.
In this paper, we present a proof of principle of the formation of pure maximally entangled states from the Greenberger-Horne-Zeilinger (GHZ) class, in the experimental context of charged quantum dots. Each qubit must be identified as a pair of quantum dots, sharing an excess electron, coupled by tunneling. The electron-electron interaction is accounted for and is responsible for the coupling between the qubits. The interplay between coherent tunneling events and many-body interaction gives rise to the formation of highly entangled states. We begin by treating the problem of encoding three qubits in a system with three pairs of quantum dots, and the numerical analysis of the exact quantum dynamics to find the conditions for the generation of the GHZ states. An effective two-level model sheds light on the role of a high-order tunneling process behind the dynamics. The action of the main decoherence process, the charge dephasing, is quantified in the process. We then evaluate the physical requirements for the dynamical generation of GHZ states in an NNN-qubit scenario, and its challenges.
In this thesis we present protocols for the polarization of nuclear spins in a quantum dot via the hyperfine interaction with a conduction band electron and give a quantitative solution to the master equation we derive. The collective interference effects limiting the polarization are studied in detail, and ways of mitigating them are proposed. At high polarization levels the electron-nuclear interaction is approximated with simple and practical (quantum optical) models, suggesting the possibility of novel coherent manipulation schemes which actively make use of the nuclei. Finally we demonstrate that even completely mixed nuclear spin ensembles can be utilized for the important task of sequentially generating entanglement between electron spins.
We propose how to generate genuine multipartite entanglement of electron spin qubits in a chain of quantum dots using the naturally available single-qubit rotations and two-qubit Heisenberg exchange interaction in the system. We show that the minimum number of required operations to generate entangled states of the GHZ, cluster, and W type scales linearly with the number of qubits and estimate the fidelities of the generated entangled cluster states. As the required single and two-qubit operations have recently been realized, our proposed scheme opens the way for experimental investigation of multipartite entanglement with electron spin qubits.
Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZ M -like states with minimal cross-talk. We introduce the M -tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZ M -like states of up to M=10 qubits within time constraints that saturate bounds on M -way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary M -tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary M -tangling power which incorporates the impact of electronic dephasing errors on the M -way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation.
We numerically study the hyperfine induced nuclear spin dynamics in a system of two coupled quantum dots in zero magnetic field. Each of the electron spins is considered to interact with an individual bath of nuclear spins via homogeneous coupling constants (all coupling coefficients being equal). In order to lower the dimension of the problem, the two baths are approximated by two single long spins. We demonstrate that the hyperfine interaction allows to utilize the nuclear baths for quantum information purposes. In particular, we show that it is possible to swap the nuclear ensembles on time scales of seconds and indicate that it might even be possible to fully entangle them. As a key result, it turns out that the larger the baths are, the more useful they become as a resource of quantum information. Interestingly, the nuclear spin dynamics strongly benefits from combining two quantum dots of different geometry to a double-dot setup.
We numerically study the hyperfine induced nuclear spin dynamics in a system of two coupled quantum dots in zero magnetic field. Each of the electron spins is considered to interact with an individual bath of nuclear spins via homogeneous coupling constants (all coupling coefficients being equal). In order to lower the dimension of the problem, the two baths are approximated by two single long spins. We demonstrate that the hyperfine interaction allows to utilize the nuclear baths for quantum information purposes. In particular, we show that it is possible to swap the nuclear ensembles on time scales of seconds and indicate that it might even be possible to fully entangle them. As a key result, it turns out that the larger the baths are, the more useful they become as a resource of quantum information. Interestingly, the nuclear spin dynamics strongly benefits from combining two quantum dots of different geometry to a double-dot setup.