Experimental measurement-device-independent quantum key distribution with uncharacterized encoding

Chao Wang; Shuang Wang; Zhen-Qiang Yin; Wei Chen; Hong-Wei Li; Chun-Mei Zhang; Yu-Yang Ding; Guang-Can Guo; Zheng-Fu Han

doi:10.1364/OL.41.005596

Optics Letters
Vol. 41,
Issue 23,
pp. 5596-5599
(2016)
•https://doi.org/10.1364/OL.41.005596

Experimental measurement-device-independent quantum key distribution with uncharacterized encoding

Chao Wang, Shuang Wang, Zhen-Qiang Yin, Wei Chen, Hong-Wei Li, Chun-Mei Zhang, Yu-Yang Ding, Guang-Can Guo, and Zheng-Fu Han

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Chao Wang, Shuang Wang, Zhen-Qiang Yin, Wei Chen, Hong-Wei Li, Chun-Mei Zhang, Yu-Yang Ding, Guang-Can Guo, and Zheng-Fu Han, "Experimental measurement-device-independent quantum key distribution with uncharacterized encoding," Opt. Lett. 41, 5596-5599 (2016)

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Table of Contents Category
- Quantum Optics
Optics & Photonics Topics
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About this Article
History
- Original Manuscript: September 23, 2016
- Revised Manuscript: October 28, 2016
- Manuscript Accepted: October 31, 2016
- Published: November 30, 2016

Abstract

Measurement-device-independent quantum key distribution (MDI QKD) is an efficient way to share secrets using untrusted measurement devices. However, the assumption on the characterizations of encoding states is still necessary in this promising protocol, which may lead to unnecessary complexity and potential loopholes in realistic implementations. Here, by using the mismatched-basis statistics, we present the first proof-of-principle experiment of MDI QKD with uncharacterized encoding sources. In this demonstration, the encoded states are only required to be constrained in a two-dimensional Hilbert space, and two distant parties (Alice and Bob) are resistant to state preparation flaws even if they have no idea about the detailed information of their encoding states. The positive final secure key rates of our system exhibit the feasibility of this novel protocol, and demonstrate its value for the application of secure communication with uncharacterized devices.

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(a)
		$μ_{Alice}$		$ν_{Alice}$		$ω_{Alice}$
$μ_{Bob}$		$1.6006 \times 10^{- 4}$		$1.6256 \times 10^{- 5}$		$3.2017 \times 10^{- 7}$
$v_{Bob}$		$1.6542 \times 10^{- 5}$		$1.5623 \times 10^{- 6}$		$3.0781 \times 10^{- 8}$
$ω_{Bob}$		$2.7830 \times 10^{- 7}$		$3.1054 \times 10^{- 8}$		$1.9177 \times 10^{- 10}$
(b)
$Y_{Z Z, L}^{1, 1}$	$9.2422 \times 10^{- 4}$		$E_{b, Z Z}^{μ, μ}$	0.0162	$p {(1 \| 2, 0)}_{L}^{1, 1}$		$8.5037 \times 10^{- 4}$
$p {(1 \| 0, 0)}_{L}^{1, 1}$	$9.8099 \times 10^{- 7}$		$p {(1 \| 0, 0)}_{U}^{1, 1}$	$1.1160 \times 10^{- 6}$	$p (1 \| 2, 0)_{U}^{1, 1}$		$9.6900 \times 10^{- 4}$
$p {(1 \| 0, 1)}_{L}^{1, 1}$	$2.1289 \times 10^{- 3}$		$p {(1 \| 0, 1)}_{U}^{1, 1}$	$2.2985 \times 10^{- 3}$	$p {(1 \| 2, 1)}_{L}^{1, 1}$		$1.0357 \times 10^{- 3}$
$p {(1 \| 1, 0)}_{L}^{1, 1}$	$2.1707 \times 10^{- 3}$		$p {(1 \| 1, 0)}_{U}^{1, 1}$	$2.3179 \times 10^{- 3}$	$p {(1 \| 2, 1)}_{U}^{1, 1}$		$1.1351 \times 10^{- 3}$
$p {(1 \| 1, 1)}_{L}^{1, 1}$	$1.2646 \times 10^{- 6}$		$p {(1 \| 1, 1)}_{U}^{1, 1}$	$1.4552 \times 10^{- 6}$	$p {(1 \| 0, 2)}_{L}^{1, 1}$		$1.2374 \times 10^{- 3}$
$p (1 \| 2, 2)_{L}^{1, 1}$	0		$p {(1 \| 2, 2)}_{U}^{1, 1}$	$4.3702 \times 10^{- 5}$	$p {(1 \| 0, 2)}_{U}^{1, 1}$		$1.3332 \times 10^{- 3}$
$p {(1 \| 1, 2)}_{L}^{1, 1}$	$1.2578 \times 10^{- 3}$		$p {(1 \| 1, 2)}_{U}^{1, 1}$	$1.3603 \times 10^{- 3}$

(a)
		$μ_{Alice}$		$ν_{Alice}$		$ω_{Alice}$
$μ_{Bob}$		$6.4880 \times 10^{- 5}$		$6.3401 \times 10^{- 6}$		$2.7025 \times 10^{- 7}$
$ν_{Bob}$		$6.4606 \times 10^{- 6}$		$5.7430 \times 10^{- 7}$		$2.0134 \times 10^{- 8}$
$ω_{Bob}$		$2.5949 \times 10^{- 7}$		$1.2983 \times 10^{- 8}$		$1.9177 \times 10^{- 10}$
(b)
$Y_{Z Z, L}^{1, 1}$	$3.2766 \times 10^{- 4}$		$E_{b, Z Z}^{μ, μ}$	0.0176	$p {(1 \| 2, 0)}_{L}^{1, 1}$		$3.5164 \times 10^{- 4}$
$p {(1 \| 0, 0)}_{L}^{1, 1}$	$1.5279 \times 10^{- 6}$		$p {(1 \| 0, 0)}_{U}^{1, 1}$	$1.5673 \times 10^{- 6}$	$p {(1 \| 2, 0)}_{U}^{1, 1}$		$3.9400 \times 10^{- 4}$
$p {(1 \| 0, 1)}_{L}^{1, 1}$	$8.5505 \times 10^{- 4}$		$p {(1 \| 0, 1)}_{U}^{1, 1}$	$9.3434 \times 10^{- 4}$	$p {(1 \| 2, 1)}_{L}^{1, 1}$		$3.3055 \times 10^{- 4}$
$p {(1 \| 1, 0)}_{L}^{1, 1}$	$8.7375 \times 10^{- 4}$		$p (1 \| 1, 0)_{U}^{1, 1}$	$9.4397 \times 10^{- 4}$	$p {(1 \| 2, 1)}_{U}^{1, 1}$		$3.8180 \times 10^{- 4}$
$p {(1 \| 1, 1)}_{L}^{1, 1}$	$3.2460 \times 10^{- 6}$		$p {(1 \| 1, 1)}_{U}^{1, 1}$	$3.2773 \times 10^{- 6}$	$p {(1 \| 0, 2)}_{L}^{1, 1}$		$3.8331 \times 10^{- 4}$
$p {(1 \| 2, 2)}_{L}^{1, 1}$	0		$p {(1 \| 2, 2)}_{U}^{1, 1}$	$9.4182 \times 10^{- 6}$	$p {(1 \| 0, 2)}_{U}^{1, 1}$		$4.2745 \times 10^{- 4}$
$p {(1 \| 1, 2)}_{L}^{1, 1}$	$3.9148 \times 10^{- 3}$		$p {(1 \| 1, 2)}_{U}^{1, 1}$	$4.2746 \times 10^{- 4}$

Distance (km)	Phase Error Rate	Final Secure Key Rate (Bits/Pulse)
0	8.4087%	$2.0848 \times 10^{- 5}$
20	8.8848%	$5.2219 \times 10^{- 6}$

(a)
		$μ_{Alice}$		$ν_{Alice}$		$ω_{Alice}$
$μ_{Bob}$		$1.6006 \times 10^{- 4}$		$1.6256 \times 10^{- 5}$		$3.2017 \times 10^{- 7}$
$v_{Bob}$		$1.6542 \times 10^{- 5}$		$1.5623 \times 10^{- 6}$		$3.0781 \times 10^{- 8}$
$ω_{Bob}$		$2.7830 \times 10^{- 7}$		$3.1054 \times 10^{- 8}$		$1.9177 \times 10^{- 10}$
(b)
$Y_{Z Z, L}^{1, 1}$	$9.2422 \times 10^{- 4}$		$E_{b, Z Z}^{μ, μ}$	0.0162	$p {(1 \| 2, 0)}_{L}^{1, 1}$		$8.5037 \times 10^{- 4}$
$p {(1 \| 0, 0)}_{L}^{1, 1}$	$9.8099 \times 10^{- 7}$		$p {(1 \| 0, 0)}_{U}^{1, 1}$	$1.1160 \times 10^{- 6}$	$p (1 \| 2, 0)_{U}^{1, 1}$		$9.6900 \times 10^{- 4}$
$p {(1 \| 0, 1)}_{L}^{1, 1}$	$2.1289 \times 10^{- 3}$		$p {(1 \| 0, 1)}_{U}^{1, 1}$	$2.2985 \times 10^{- 3}$	$p {(1 \| 2, 1)}_{L}^{1, 1}$		$1.0357 \times 10^{- 3}$
$p {(1 \| 1, 0)}_{L}^{1, 1}$	$2.1707 \times 10^{- 3}$		$p {(1 \| 1, 0)}_{U}^{1, 1}$	$2.3179 \times 10^{- 3}$	$p {(1 \| 2, 1)}_{U}^{1, 1}$		$1.1351 \times 10^{- 3}$
$p {(1 \| 1, 1)}_{L}^{1, 1}$	$1.2646 \times 10^{- 6}$		$p {(1 \| 1, 1)}_{U}^{1, 1}$	$1.4552 \times 10^{- 6}$	$p {(1 \| 0, 2)}_{L}^{1, 1}$		$1.2374 \times 10^{- 3}$
$p (1 \| 2, 2)_{L}^{1, 1}$	0		$p {(1 \| 2, 2)}_{U}^{1, 1}$	$4.3702 \times 10^{- 5}$	$p {(1 \| 0, 2)}_{U}^{1, 1}$		$1.3332 \times 10^{- 3}$
$p {(1 \| 1, 2)}_{L}^{1, 1}$	$1.2578 \times 10^{- 3}$		$p {(1 \| 1, 2)}_{U}^{1, 1}$	$1.3603 \times 10^{- 3}$

(a)
		$μ_{Alice}$		$ν_{Alice}$		$ω_{Alice}$
$μ_{Bob}$		$6.4880 \times 10^{- 5}$		$6.3401 \times 10^{- 6}$		$2.7025 \times 10^{- 7}$
$ν_{Bob}$		$6.4606 \times 10^{- 6}$		$5.7430 \times 10^{- 7}$		$2.0134 \times 10^{- 8}$
$ω_{Bob}$		$2.5949 \times 10^{- 7}$		$1.2983 \times 10^{- 8}$		$1.9177 \times 10^{- 10}$
(b)
$Y_{Z Z, L}^{1, 1}$	$3.2766 \times 10^{- 4}$		$E_{b, Z Z}^{μ, μ}$	0.0176	$p {(1 \| 2, 0)}_{L}^{1, 1}$		$3.5164 \times 10^{- 4}$
$p {(1 \| 0, 0)}_{L}^{1, 1}$	$1.5279 \times 10^{- 6}$		$p {(1 \| 0, 0)}_{U}^{1, 1}$	$1.5673 \times 10^{- 6}$	$p {(1 \| 2, 0)}_{U}^{1, 1}$		$3.9400 \times 10^{- 4}$
$p {(1 \| 0, 1)}_{L}^{1, 1}$	$8.5505 \times 10^{- 4}$		$p {(1 \| 0, 1)}_{U}^{1, 1}$	$9.3434 \times 10^{- 4}$	$p {(1 \| 2, 1)}_{L}^{1, 1}$		$3.3055 \times 10^{- 4}$
$p {(1 \| 1, 0)}_{L}^{1, 1}$	$8.7375 \times 10^{- 4}$		$p (1 \| 1, 0)_{U}^{1, 1}$	$9.4397 \times 10^{- 4}$	$p {(1 \| 2, 1)}_{U}^{1, 1}$		$3.8180 \times 10^{- 4}$
$p {(1 \| 1, 1)}_{L}^{1, 1}$	$3.2460 \times 10^{- 6}$		$p {(1 \| 1, 1)}_{U}^{1, 1}$	$3.2773 \times 10^{- 6}$	$p {(1 \| 0, 2)}_{L}^{1, 1}$		$3.8331 \times 10^{- 4}$
$p {(1 \| 2, 2)}_{L}^{1, 1}$	0		$p {(1 \| 2, 2)}_{U}^{1, 1}$	$9.4182 \times 10^{- 6}$	$p {(1 \| 0, 2)}_{U}^{1, 1}$		$4.2745 \times 10^{- 4}$
$p {(1 \| 1, 2)}_{L}^{1, 1}$	$3.9148 \times 10^{- 3}$		$p {(1 \| 1, 2)}_{U}^{1, 1}$	$4.2746 \times 10^{- 4}$

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Optics Letters