Remote implementation of single-qubit operations via hyperentangled states with cross-Kerr nonlinearity

Xian-Fang Jiao; Ping Zhou; Shu-Xin Lv

doi:10.1364/JOSAB.36.000867

Journal of the Optical Society of America B
Vol. 36,
Issue 4,
pp. 867-875
(2019)
•https://doi.org/10.1364/JOSAB.36.000867

Remote implementation of single-qubit operations via hyperentangled states with cross-Kerr nonlinearity

Xian-Fang Jiao, Ping Zhou, and Shu-Xin Lv

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Xian-Fang Jiao, Ping Zhou, and Shu-Xin Lv, "Remote implementation of single-qubit operations via hyperentangled states with cross-Kerr nonlinearity," J. Opt. Soc. Am. B 36, 867-875 (2019)

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Table of Contents Category
- Quantum Optics
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: December 13, 2018
- Revised Manuscript: January 25, 2019
- Manuscript Accepted: January 30, 2019
- Published: March 8, 2019

Abstract

Quantum information processing via hyperentanglement can improve the quantum channel capacity for long-distance quantum communication and large-scale quantum communication networks. Some important works have been presented in quantum remote state preparation with hyperentangled states. However, the protocols for quantum operation remote implementation are based on quantum systems encoded in one degree of freedom. We present a quantum operation remote implementation protocol for arbitrary single-qubit operations with two-photon hyperentangled states via cross-Kerr nonlinearities. Moreover, we discuss the scheme for parallel remote implementation of partially unknown quantum operations via two-photon hyperentangled states.

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Equations (30)

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$R_{1}$	$R_{2}$	State	$U_{r}$
$\| α_{1} e^{\pm i θ} ⟩$	$\| α_{2} ⟩$	$β_{0} \| c_{0} ⟩ + β_{1} \| c_{1} ⟩$	I
$\| α_{1} e^{\pm i θ} ⟩$	$\| α_{2} e^{i θ_{1}} ⟩$	$β_{0} \| c_{0} ⟩ - β_{1} \| c_{1} ⟩$	$σ_{z}^{s}$
$\| α_{1} e^{\pm i θ} ⟩$	$\| α_{2} e^{i θ_{2}} ⟩$	$β_{0} \| c_{0} ⟩ - β_{1} \| c_{1} ⟩$	$σ_{z}^{s}$
$\| α_{1} e^{\pm i θ} ⟩$	$\| α_{2} e^{i (θ_{1} + θ_{2})} ⟩$	$β_{0} \| c_{0} ⟩ + β_{1} \| c_{1} ⟩$	I
$\| α_{1} ⟩$	$\| α_{2} ⟩$	$β_{0} \| c_{1} ⟩ + β_{1} \| c_{0} ⟩$	$σ_{x}^{s}$
$\| α_{1} ⟩$	$\| α_{2} e^{i θ_{1}} ⟩$	$β_{0} \| c_{1} ⟩ - β_{1} \| c_{0} ⟩$	$σ_{z}^{s} σ_{x}^{s}$
$\| α_{1} ⟩$	$\| α_{2} e^{i θ_{2}} ⟩$	$β_{0} \| c_{1} ⟩ - β_{1} \| c_{0} ⟩$	$σ_{z}^{s} σ_{x}^{s}$
$\| α_{1} ⟩$	$\| α_{2} e^{i (θ_{1} + θ_{2})} ⟩$	$β_{0} \| c_{1} ⟩ + β_{1} \| c_{0} ⟩$	$σ_{x}^{s}$

$R_{2}$	$R_{3}$	State	$U_{r}$
$\| α_{2} ⟩$	$\| α_{3} ⟩$	${(σ_{x}^{s})}^{l_{2}} U_{l_{2}} {\| χ ⟩}^{s}$	${(σ_{x}^{s})}^{l_{2}}$
$\| α_{2} ⟩$	$\| α_{3} e^{i θ_{2}} ⟩$	${(σ_{x}^{s})}^{l_{2}} σ_{z}^{s} U_{l_{2}} {\| χ ⟩}^{s}$	$σ_{z}^{s} {(σ_{x}^{s})}^{l_{2}}$
$\| α_{2} e^{i θ_{1}} ⟩$	$\| α_{3} ⟩$	${(σ_{x}^{s})}^{l_{2}} σ_{z}^{s} U_{l_{2}} {\| χ ⟩}^{s}$	$σ_{z}^{s} {(σ_{x}^{s})}^{l_{2}}$
$\| α_{2} e^{i θ_{1}} ⟩$	$\| α_{3} e^{i θ_{2}} ⟩$	${(σ_{x}^{s})}^{l_{2}} U_{l_{2}} {\| χ ⟩}^{s}$	${(σ_{x}^{s})}^{l_{2}}$

$R_{2}$	$R_{3}$	State	$U_{r}$
$\| H ⟩$	$\| H ⟩$	${(σ_{x}^{p})}^{l_{1}} U_{l_{1}} {\| χ ⟩}^{p}$	${(σ_{x}^{p})}^{l_{1}}$
$\| H ⟩$	$\| V ⟩$	${(σ_{x}^{p})}^{l_{1}} σ_{z}^{p} U_{l_{1}} {\| χ ⟩}^{p}$	$σ_{z}^{p} {(σ_{x}^{p})}^{l_{1}}$
$\| V ⟩$	$\| H ⟩$	${(σ_{x}^{p})}^{l_{1}} σ_{z}^{p} U_{l_{1}} {\| χ ⟩}^{p}$	$σ_{z}^{p} {(σ_{x}^{p})}^{l_{1}}$
$\| V ⟩$	$\| V ⟩$	${(σ_{x}^{p})}^{l_{1}} U_{l_{1}} {\| χ ⟩}^{p}$	${(σ_{x}^{p})}^{l_{1}}$

$R_{1}$	$R_{2}$	State	$U_{r}$
$\| α_{1} e^{\pm i θ} ⟩$	$\| α_{2} ⟩$	$β_{0} \| c_{0} ⟩ + β_{1} \| c_{1} ⟩$	I
$\| α_{1} e^{\pm i θ} ⟩$	$\| α_{2} e^{i θ_{1}} ⟩$	$β_{0} \| c_{0} ⟩ - β_{1} \| c_{1} ⟩$	$σ_{z}^{s}$
$\| α_{1} e^{\pm i θ} ⟩$	$\| α_{2} e^{i θ_{2}} ⟩$	$β_{0} \| c_{0} ⟩ - β_{1} \| c_{1} ⟩$	$σ_{z}^{s}$
$\| α_{1} e^{\pm i θ} ⟩$	$\| α_{2} e^{i (θ_{1} + θ_{2})} ⟩$	$β_{0} \| c_{0} ⟩ + β_{1} \| c_{1} ⟩$	I
$\| α_{1} ⟩$	$\| α_{2} ⟩$	$β_{0} \| c_{1} ⟩ + β_{1} \| c_{0} ⟩$	$σ_{x}^{s}$
$\| α_{1} ⟩$	$\| α_{2} e^{i θ_{1}} ⟩$	$β_{0} \| c_{1} ⟩ - β_{1} \| c_{0} ⟩$	$σ_{z}^{s} σ_{x}^{s}$
$\| α_{1} ⟩$	$\| α_{2} e^{i θ_{2}} ⟩$	$β_{0} \| c_{1} ⟩ - β_{1} \| c_{0} ⟩$	$σ_{z}^{s} σ_{x}^{s}$
$\| α_{1} ⟩$	$\| α_{2} e^{i (θ_{1} + θ_{2})} ⟩$	$β_{0} \| c_{1} ⟩ + β_{1} \| c_{0} ⟩$	$σ_{x}^{s}$

$R_{2}$	$R_{3}$	State	$U_{r}$
$\| α_{2} ⟩$	$\| α_{3} ⟩$	${(σ_{x}^{s})}^{l_{2}} U_{l_{2}} {\| χ ⟩}^{s}$	${(σ_{x}^{s})}^{l_{2}}$
$\| α_{2} ⟩$	$\| α_{3} e^{i θ_{2}} ⟩$	${(σ_{x}^{s})}^{l_{2}} σ_{z}^{s} U_{l_{2}} {\| χ ⟩}^{s}$	$σ_{z}^{s} {(σ_{x}^{s})}^{l_{2}}$
$\| α_{2} e^{i θ_{1}} ⟩$	$\| α_{3} ⟩$	${(σ_{x}^{s})}^{l_{2}} σ_{z}^{s} U_{l_{2}} {\| χ ⟩}^{s}$	$σ_{z}^{s} {(σ_{x}^{s})}^{l_{2}}$
$\| α_{2} e^{i θ_{1}} ⟩$	$\| α_{3} e^{i θ_{2}} ⟩$	${(σ_{x}^{s})}^{l_{2}} U_{l_{2}} {\| χ ⟩}^{s}$	${(σ_{x}^{s})}^{l_{2}}$

Abstract

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Figures (4)

Tables (3)

Equations (30)

Journal of the Optical Society of America B