A quantum secure direct communication scheme based on intermediate-basis

doi:10.1007/s11467-023-1284-4

Front. Phys.

2023, Vol. 18

Issue (5) : 51301 https://doi.org/10.1007/s11467-023-1284-4

RESEARCH ARTICLE

A quantum secure direct communication scheme based on intermediate-basis

Kexin Liang^1,², Zhengwen Cao^1,²(

), Xinlei Chen¹, Lei Wang¹, Geng Chai¹(

), Jinye Peng¹

¹. Laboratory of Quantum Information & Technology (QIT), School of Information Science and Technology, Northwest University, Xi’an 710127, China
². State Key Laboratory of Integrated Services Networks (Xidian University), Xi’an 710071, China

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Abstract

Quantum secure direct communication (QSDC) is a method of communication that transmits secret information directly through a quantum channel. This paper proposes a two-step QSDC scheme based on intermediate-basis, in which the intermediate-basis Einstein−Podolsky−Rosen (EPR) pairs can assist to detect channel security and help encode information. Specifically, the intermediate-basis EPR pairs reduce the probability of Eve choosing the correct measurement basis in the first step, enhancing the security of the system. Moreover, they encode information together with information EPR pairs to improve the transmission efficiency in the second step. We consider the security of the protocol under coherent attack when Eve takes different dimensions of the auxiliary system. The simulation results show that intermediate-basis EPR pairs can lower the upper limit of the amount of information that Eve can steal in both attack scenarios. Therefore, the proposed protocol can ensure that the legitimate parties get more confidential information and improve the transmission efficiency.

Keywords quantum secure direct communication two-step intermediate-basis

Corresponding Author(s): Zhengwen Cao,Geng Chai

About author:

*These authors equally shared correspondence to this manuscript.

Issue Date: 28 April 2023

Cite this article:

Kexin Liang,Zhengwen Cao,Xinlei Chen, et al. A quantum secure direct communication scheme based on intermediate-basis[J]. Front. Phys. , 2023, 18(5): 51301.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1284-4
https://academic.hep.com.cn/fop/EN/Y2023/V18/I5/51301

Fig.1 A QSDC scheme based on intermediate-basis. (

U

: A unitary operation for encoding. The red balls refer to information EPR pairs

| ψ ? ?

, and the green balls refer to intermediate-basis EPR pairs

| ψ θ i ? ?

. Black dashed frame represents these particles are chosen for channel security detection and blue dashed frame represents these particles are used for channel secondary detection.)

Fig.2 The relationship between intermediate basis and

X

basis and

Z

basis. (

| H ? = | 0 ?, | V ? = | 1 ?, | D ? = | + ?, | A ? = | ? ?,

and the shaded part is the effective range of

θ i

Entangled pair	Alice’s encoding	Information	Bob’s decoding

$\| ψ ? ?$	$U 1$	000	$\| ψ ? ?$
	$U 2$	001	$\| ψ + ?$
	$U 3$	010	$\| Φ ? ?$
	$U 4$	011	$\| Φ + ?$
$\| ψ θ i ? ?$	$U 1$	100	$\| ψ θ i ? ?$
	$U 2$	101	$\| ψ θ i + ?$
	$U 3$	110	$\| Φ θ i + ?$
	$U 4$	111	$\| Φ θ i ? ?$

Tab.1 Summary of Alice’s encoding and Bob’s decoding.

Fig.3 Wiretap channel model. The model comprises a transmitter, a legitimate receiver, and an eavesdropper. The channel between transmitter and legitimate receiver is the main channel, and the channel between transmitter and eavesdropper is the eavesdropper’s channel.

Fig.4 The relation of channel capacity and the value of

S C H S H

. In (a), based on the starting positions on the left, the lines from top to bottom are the capacity of the wiretap channel without intermediate-basis EPR pairs, the capacity of the wiretap channel with intermediate-basis EPR pairs, the capacity of the main channel, the capacity of the secrecy channel with intermediate-basis EPR pairs, and the capacity of the secrecy channel without intermediate-basis EPR pairs. In (b) and (c), based on the starting positions on the left, the lines from top to bottom are the capacity of the main channel, the capacity of the wiretap channel without intermediate-basis EPR pairs, the capacity of the wiretap channel with intermediate-basis EPR pairs, the capacity of the secrecy channel with intermediate-basis EPR pairs, and the capacity of the secrecy channel without intermediate-basis EPR pairs. Simulation parameters: reception rates

Q B

and

Q E

are all set to 1.

Fig.5 Eve’s attack capability with different auxiliary systems.

Fig.6 The relation of channel capacity and the value of

S C H S H

. In (a), the lines from top to bottom are the capacity of the wiretap channel without intermediate-basis EPR pairs, the capacity of the wiretap channel with intermediate-basis EPR pairs, the capacity of the main channel, the capacity of the secrecy channel with intermediate-basis EPR pairs, and the capacity of the secrecy channel without intermediate-basis EPR pairs. In (b), the lines from top to bottom are the capacity of the wiretap channel without intermediate-basis EPR pairs, the capacity of the main channel, the capacity of the wiretap channel with intermediate-basis EPR pairs, the capacity of the secrecy channel with intermediate-basis EPR pairs, and the capacity of the secrecy channel without intermediate-basis EPR pairs. In (c), based on the starting positions on the left, the lines from top to bottom are the capacity of the main channel, the capacity of the secrecy channel with intermediate-basis EPR pairs, the capacity of the secrecy channel without intermediate-basis EPR pairs, the capacity of the wiretap channel without intermediate-basis EPR pairs, and the capacity of the wiretap channel with intermediate-basis EPR pairs. Simulation parameters: reception rates

Q B

and

Q E

are all set to 1.

	The original two-step protocol	The proposed protocol
Probability of Eve guessing right	$12$	$13$
Upper bound of the amount of secret information stole by Eve	Higher	Lower
Necessary quantum resource	$\| ψ ? ?$	$\| ψ θ i ? ?$ , $\| ψ ? ?$
Encoding methods	4 kinds	8 kinds
Encoding efficiency	2 bit per operation	3 bit per operation

Tab.2 Comparison of the advantages and disadvantages of the new protocol and the original two-step protocol.

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