Room-temperature storage of quantum entanglement using decoherence-free subspace in a solid-state spin system

F. Wang, Y.-Y. Huang, Z.-Y. Zhang, C. Zu, P.-Y. Hou, X.-X. Yuan, W.-B. Wang, W.-G. Zhang, L. He, X.-Y. Chang, and L.-M. Duan

Phys. Rev. B 96, 134314 – Published 31 October 2017

Abstract

We experimentally demonstrate room-temperature storage of quantum entanglement using two nuclear spins weakly coupled to the electronic spin carried by a single nitrogen-vacancy center in diamond. We realize universal quantum gate control over the three-qubit spin system and produce entangled states in the decoherence-free subspace of the two nuclear spins. By injecting arbitrary collective noise, we demonstrate that the decoherence-free entangled state has coherence time longer than that of other entangled states by an order of magnitude in our experiment.

Received 14 June 2017
Revised 20 August 2017

DOI:https://doi.org/10.1103/PhysRevB.96.134314

Physics Subject Headings (PhySH)

Quantum control Quantum entanglement Quantum information with solid state qubits Quantum memories

Nitrogen vacancy centers in diamond

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

F. Wang¹, Y.-Y. Huang¹, Z.-Y. Zhang^1,2, C. Zu¹, P.-Y. Hou¹, X.-X. Yuan¹, W.-B. Wang¹, W.-G. Zhang¹, L. He¹, X.-Y. Chang¹, and L.-M. Duan^1,2

¹Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, PR China
²Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

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Vol. 96, Iss. 13 — 1 October 2017

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Figure 1
Experimental system. (a) The NV electronic spin (red) and the coupled ${}^{13}C$ spin bath (blue). Entanglement states are stored in two isolated weakly coupled ${}^{13}C$ nuclear spins. (b) Energy structure of the NV electronic spin and a weakly coupled nuclear spin. Nuclear spin sublevels $| ↑ 〉$ and $| ↓ 〉$ are split by Zeeman shift $(ω_{L})$ and hyperfine interaction $(A_{z z}, A_{x z})$ with $ω_{0} = ω_{L} (m_{s} = 0), ω_{\pm 1} = \sqrt{{(A_{z z} \mp ω_{L})}^{2} + A_{x z}^{2}} (m_{s} = \pm 1)$ .
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Figure 2
Calibration of the nuclear spin hyperfine interaction parameters. (a) Gate sequence to scan the resonant frequency of nuclear spins with the electronic spin set at $m_{s} = + 1, 0, - 1$ states, respectively. The nuclear spin is initialized by swapping the electronic spin polarization onto the nuclear spin. Electronic spin is reset to $| 0 〉$ or $| \pm 1 〉$ state using a 350 ns green laser or an additional $π$ rotation afterwards. A rf pulse with a duration of $600 μ s$ and a scanning frequency is then implemented on the nuclear spin to trigger spin flips at resonant frequency. The final state readout is accomplished by swapping the nuclear spin state back onto the electronic spin. (b) Probability of electronic spin in $m_{s} = 0$ state $(P_{0})$ as a function of the rf frequency with the electronic spin at $m_{s} = 0, - 1, + 1$ states, respectively, for nuclear spin 1. Solid lines are the Gaussian fits. See the Supplemental Material for results on the nuclear spin 2 [45].
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Figure 3
Characterization of the conditional $X$ gate on nuclear spins 1 and 2. See the Supplemental Material for results on unconditional gates [45]. (a) Experimental scheme to characterize the gate fidelity. The nuclear spin is polarized by swapping the electronic spin polarization onto the nuclear spin. An additional $π$ rotation is applied to set the electronic spin to $m_{s} = - 1$ state. After that, the desired gate (conditional $X$ gate) is applied on the nuclear spin for $N$ times $(N = 1, \dots, 10)$ with the electronic spin at $m_{s} = 0$ or $m_{s} = - 1$ before measuring the nuclear spin on the $Y$ basis. (b) and (c) Experimental results of conditional $X$ gate on the nuclear spin 1 and 2, respectively. The nuclear spin rotates on the opposite direction of the $X$ axis with the electronic spin at $m_{s} = 0, - 1$ states. Solid lines are fits by the function $sin (2 π N / 4) (1 - b N)$ with $b = 0.012$ and a standard deviation of $σ = 0.011$ in (b) and $b = 0.025$ and a standard deviation of $σ = 0.014$ in (c). The results are without correction of initialization and detection error.
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Figure 4
Preparation and detection of entangled states between the nuclear spins. (a) Gate sequence to prepare entangled states between nuclear spins at room temperature. Entanglement is first generated between the nuclear spin 2 and the electronic spin. By swapping the electronic spin with the nuclear spin 1, entanglement between nuclear spins is produced. A subsequent $π / 2$ rotation is applied to prepare the entangled state in the DFS. The phase $ϕ$ of the operation in red is controlled to produce $| T 〉$ state $(ϕ = 0)$ or $| S 〉$ state $(ϕ = π)$ . The readout is performed by quantum state tomography on the two nuclear spins [45]. (b) and (c) Quantum state tomography results for $| S 〉$ state (b) and $| T 〉$ state (c). Black bar describes the simulation result [45], blue (green) bar is the experiment data for $| S 〉$ $(| T 〉)$ state without correction of initialization and readout errors.
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Figure 5
Decay of the entanglement fidelity under various noise environments. (a) Entanglement fidelity as a function of the storage time $t$ under collective dephasing noise. Solid lines are fits to $exp (- t / T_{est})$ with $T_{est} = 2.24$ ms and a standard deviation of $σ = 153 μ s$ for $| S 〉$ state (blue) and $T_{est} = 2.29$ ms and a standard deviation of $σ = 232 μ s$ for $| T 〉$ state (green). The fitting curves saturate at 0.35, which corresponds to the fidelity of the final state when all the coherence terms drop to zero. Due to the limited fidelity for initial state preparation, the population is not given by an identity matrix, so the saturation fidelity is 0.35 instead of 0.5. (b) Entanglement fidelity as a function of the storage time $t$ under general collective noise. Solid lines are fits to $exp (- t / T_{est})$ with $T_{est} = 2.18$ ms and a standard deviation of $σ = 366 μ s$ for $| S 〉$ state (blue) and $T_{est} = 360 μ s$ and a standard deviation of $σ = 20 μ s$ for $| T 〉$ state (green).
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