多方控制量子通信协议

doi:10.11959/j.issn.1000-436x.2015221

通信学报 ›› 2015, Vol. 36 ›› Issue (6): 139-148.doi: 10.11959/j.issn.1000-436x.2015221

多方控制量子通信协议

常利伟^1,²,郑世慧^1,²,谷利泽^1,²,雷敏^1,²,杨义先^1,²

¹ 北京邮电大学信息安全中心，北京 100876
² 北京邮电大学灾备技术国家工程实验室，北京 100876

出版日期:2015-06-25 发布日期:2017-05-11
基金资助:
国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;中央高校基金资助项目;中央高校基金资助项目

Multi-party controlled quantum communication protocol

Li-wei CHANG^1,²,Shi-hui ZHENG^1,²,Li-ze GU^1,²,Min LEI^1,²,Yi-xian YANG^1,²

¹ Information Security Research Center,Beijing University of Posts and Telecommunications,Beijing 100876,China
² National Engineering Laboratory for Disaster Backup and Recovery,Beijing University of Posts and Telecommunications,Beijing 100876,China

Online:2015-06-25 Published:2017-05-11
Supported by:
The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;Fundamental Research Funds for the Central Universities;Fundamental Research Funds for the Central Universities

摘要/Abstract

摘要：

为了满足远距离多节点量子网络的需求，分别利用最大纠缠信道和部分纠缠信道构造了2个多方控制量子通信协议。最大纠缠信道时，利用投影测量实现多方控制四粒子X-态远程制备; 部分纠缠信道时，利用联合酉操作和最优POVM实现多方控制四粒子X-态远程制备。理论推导表明，第一个协议的效率达到100%且优于其他协议，第二协议的效率被有效提高且2种测量方法的构造方法可被用于同类协议。

关键词: 多方控制协议, 四粒子X-态, 联合酉操作, 最优POVM测量

Abstract:

In order to satisfy the requirements of long-distance multi-node quantum networks，two multi-party controlledquantum communication protocols are put forward via maximally and partially entangled quantum channels.For the maximally entangled channels,projective measurements are used to realizemulti-party controlled joint remote preparation of an arbitrary four-qubitX-state.For the partially entangled channels,collective unitary operations and optimal positive operator-valued measures are used to realize multi-party controlled joint remote preparation of an arbitrary four-qubitX-state.The theoretical analysis shows that the efficiency of the first scheme can be up to 100% which is suprior to that of others.In addition,the efficiency of the second scheme is effectively improved and the way to be used to construct two kinds of measurement methods can be utilized in the similar protocols.

Key words: multiparty controlled protocol, four-qubit X-state, joint unitary operation, optimal positive operator-valued measure

常利伟,郑世慧,谷利泽,雷敏,杨义先. 多方控制量子通信协议[J]. 通信学报, 2015, 36(6): 139-148.

Li-wei CHANG,Shi-hui ZHENG,Li-ze GU,Min LEI,Yi-xian YANG. Multi-party controlled quantum communication protocol[J]. Journal on Communications, 2015, 36(6): 139-148.

图/表 5

图1

图2

表1

接收者Dick应实施的恢复操作"

m₁	m₂	U_D
00	00	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes σ_{4 N + 2}^{z} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x} σ_{4 N + 4}^{z}$
00	01	$σ_{4 N + 1}^{z} \otimes σ_{4 N + 2}^{x} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x} σ_{4 N + 4}^{z}$
00	10	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes σ_{4 N + 2}^{z} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x}$
00	11	$σ_{4 N + 1}^{z} \otimes σ_{4 N + 2}^{x} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x}$
01	00	$σ_{4 N + 1}^{z} \otimes σ_{4 N + 2}^{x} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x} σ_{4 N + 4}^{z}$
01	01	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes σ_{4 N + 2}^{z} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x} σ_{4 N + 4}^{z}$
01	10	$σ_{4 N + 1}^{z} \otimes σ_{4 N + 2}^{x} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x}$
01	11	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes σ_{4 N + 2}^{z} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x}$
10	00	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x} σ_{4 N + 4}^{z}$
10	01	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes σ_{4 N + 3}^{z} \otimes σ_{4 N + 4}^{x}$
10	10	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x}$
10	11	$σ_{4 N + 1}^{z} \otimes σ_{4 N + 2}^{x} σ_{4 N + 2}^{x} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x}$
11	00	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes σ_{4 N + 3}^{z} \otimes σ_{4 N + 4}^{x}$
11	01	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x} σ_{4 N + 4}^{z}$
11	10	$σ_{4 N + 1}^{z} \otimes σ_{4 N + 2}^{x} σ_{4 N + 2}^{z} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x}$
11	11	$I_{4 N + 1} \otimes σ_{4 N + 2}^{x} \otimes I_{4 N + 3} \otimes σ_{4 N + 4}^{x}$

表1

图3

表2

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方法	恢复操作维数	辅助粒子个数	协议成功效率
方法1	16	1	²16\|a₁ b₁ c₁ d₁\|
方法2	8	3	16μ ²

多方控制量子通信协议

Multi-party controlled quantum communication protocol

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