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Journals >Photonics Research >Volume 6 >Issue 5 >Page 479 > Article

Photonics Research
Vol. 6, Issue 5, 479 (2018)

Generation of a continuous-variable quadripartite cluster state multiplexed in the spatial domain

Chunxiao Cai^1、2, Long Ma^1、2, Juan Li^1、2, Hui Guo^1、2, Kui Liu^1、2, Hengxin Sun^1、2, Rongguo Yang^1、2, and Jiangrui Gao^1、2、*

Author Affiliations

¹State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China

²Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

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DOI: 10.1364/PRJ.6.000479 Cite this Article Set citation alerts

Chunxiao Cai, Long Ma, Juan Li, Hui Guo, Kui Liu, Hengxin Sun, Rongguo Yang, Jiangrui Gao. Generation of a continuous-variable quadripartite cluster state multiplexed in the spatial domain[J]. Photonics Research, 2018, 6(5): 479 Copy Citation Text

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Abstract

As a highly entangled quantum network, the cluster state has the potential for greater information capacity and use in measurement-based quantum computation. Here, we report generating a continuous-variable quadripartite “square” cluster state of multiplexing orthogonal spatial modes in a single optical parametric amplifier (OPA), and further improve the quality of entanglement by optimizing the pump profile. We produce multimode entanglement of two first-order Hermite–Gauss modes within one beam in a single multimode OPA and transform it into a cluster state by phase correction. Furthermore, the pump-profile dependence of the entanglement of this state is explored. Compared with fundamental mode pumping, an enhancement of approximately 33% is achieved using the suitable pump-profile mode. Our approach is potentially scalable to multimode entanglement in the spatial domain. Such spatial cluster states may contribute to future schemes in spatial quantum information processing.

Keywords

Nonlinear optics, parametric processes Squeezed states

H_{int} = i ℏ χ \sum_{k} ({\hat{a}}_{p} {\hat{a}}_{+ 1}^{i †} {\hat{a}}_{- 1}^{s †} + {\hat{a}}_{p} {\hat{a}}_{- 1}^{i †} {\hat{a}}_{+ 1}^{s †} + h.c),

(1)

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H_{int} = i ℏ χ \sum_{k} ({\hat{a}}_{p} {\hat{a}}_{10}^{i †} {\hat{a}}_{10}^{s †} + {\hat{a}}_{p} {\hat{a}}_{01}^{i †} {\hat{a}}_{01}^{s †} + h.c),

(2)

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V ({\hat{X}}_{01}^{i} + {\hat{X}}_{01}^{s}) < 1,

(3a)

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V ({\hat{Y}}_{01}^{i} - {\hat{Y}}_{01}^{s}) < 1,

(3b)

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V ({\hat{X}}_{10}^{i} + {\hat{X}}_{10}^{s}) < 1,

(3c)

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V ({\hat{Y}}_{10}^{i} - {\hat{Y}}_{10}^{s}) < 1,

(3d)

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{\hat{X}}_{01}^{s} = ({\hat{Y}}_{135 °}^{s} + {\hat{Y}}_{45 °}^{s}) / \sqrt{2},

(4a)

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{\hat{Y}}_{01}^{s} = - ({\hat{X}}_{135 °}^{s} + {\hat{X}}_{45 °}^{s}) / \sqrt{2},

(4b)

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{\hat{X}}_{10}^{s} = ({\hat{Y}}_{135 °}^{s} - {\hat{Y}}_{45 °}^{s}) / \sqrt{2},

(4c)

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{\hat{Y}}_{10}^{s} = - ({\hat{X}}_{135 °}^{s} - {\hat{X}}_{45 °}^{s}) / \sqrt{2} .

(4d)

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V ({\hat{Y}}_{01}^{i} + \frac{1}{\sqrt{2}} {\hat{X}}_{135 °}^{s} + \frac{1}{\sqrt{2}} {\hat{X}}_{45 °}^{s}) < 1,

(5a)

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V ({\hat{Y}}_{10}^{i} + \frac{1}{\sqrt{2}} {\hat{X}}_{135 °}^{s} - \frac{1}{\sqrt{2}} {\hat{X}}_{45 °}^{s}) < 1,

(5b)

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V ({\hat{Y}}_{45 °}^{s} + \frac{1}{\sqrt{2}} {\hat{X}}_{01}^{i} - \frac{1}{\sqrt{2}} {\hat{X}}_{10}^{i}) < 1,

(5c)

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V ({\hat{Y}}_{135 °}^{s} + \frac{1}{\sqrt{2}} {\hat{X}}_{01}^{i} + \frac{1}{\sqrt{2}} {\hat{X}}_{10}^{i}) < 1,

(5d)

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\hat{Y} - A \hat{X} \to 0,

(6)

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V ({\hat{Y}}_{01}^{i} - {\hat{Y}}_{01}^{s}) < 1,

(7a)

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V ({\hat{Y}}_{10}^{i} - {\hat{Y}}_{10}^{s}) < 1,

(7b)

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V ({\hat{Y}}_{45 °}^{i} - {\hat{Y}}_{45 °}^{s}) < 1,

(7c)

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V ({\hat{Y}}_{135 °}^{i} - {\hat{Y}}_{135 °}^{s}) < 1 .

(7d)

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Γ = \int_{- \infty}^{+ \infty} \frac{ν^{p} (\vec{r}) μ^{s} (\vec{r}) μ^{i} (\vec{r})}{α} d \vec{r},

(8)

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Γ_{00} = \int_{- \infty}^{+ \infty} \frac{ν_{00} (\vec{r}) μ_{01 / 10}^{2} (\vec{r})}{\sqrt{\int_{- \infty}^{+ \infty} μ_{01 / 10}^{4} (\vec{r}) d \vec{r}}} d \vec{r} = \sqrt{\frac{1}{3}},

(9a)

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Γ_{02 / 20} = \int_{- \infty}^{+ \infty} \frac{ν_{02 / 20} (\vec{r}) μ_{01 / 10}^{2} (\vec{r})}{\sqrt{\int_{- \infty}^{+ \infty} μ_{01 / 10}^{4} (\vec{r}) d \vec{r}}} d \vec{r} = \sqrt{\frac{2}{3}},

(9b)

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V ({\hat{Y}}_{01}^{i} - {\hat{Y}}_{01}^{s}) = 0.62 \pm 0.02 < 1,

(10a)

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V ({\hat{Y}}_{10}^{i} - {\hat{Y}}_{10}^{s}) = 0.59 \pm 0.02 < 1,

(10b)

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V ({\hat{Y}}_{45 °}^{i} - {\hat{Y}}_{45 °}^{s}) = 0.64 \pm 0.02 < 1,

(10c)

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V ({\hat{Y}}_{135 °}^{i} - {\hat{Y}}_{135 °}^{s}) = 0.61 \pm 0.02 < 1 .

(10d)

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V ({\hat{Y}}_{01}^{i} - {\hat{Y}}_{01}^{s}) = 0.48 \pm 0.02 < 1,

(11a)

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V ({\hat{Y}}_{10}^{i} - {\hat{Y}}_{10}^{s}) = 0.43 \pm 0.02 < 1,

(11b)

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V ({\hat{Y}}_{45 °}^{i} - {\hat{Y}}_{45 °}^{s}) = 0.48 \pm 0.02 < 1,

(11c)

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V ({\hat{Y}}_{135 °}^{i} - {\hat{Y}}_{135 °}^{s}) = 0.47 \pm 0.02 < 1 .

(11d)

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References (36)

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Chunxiao Cai, Long Ma, Juan Li, Hui Guo, Kui Liu, Hengxin Sun, Rongguo Yang, Jiangrui Gao. Generation of a continuous-variable quadripartite cluster state multiplexed in the spatial domain[J]. Photonics Research, 2018, 6(5): 479

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