Robust quantum dialogue based on a shared auxiliary logical Bell state against collective noise

TianYu YE

doi:10.1360/SSPMA2014-00289

SCIENTIA SINICA Physica, Mechanica & Astronomica

SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 45, Issue 4: 040301(2015) https://doi.org/10.1360/SSPMA2014-00289

Robust quantum dialogue based on a shared auxiliary logical Bell state against collective noise

TianYu YE^*

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ReceivedJul 28, 2014
AcceptedSep 10, 2014
PublishedJan 30, 2015

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Abstract

本文分别提出两个抵抗集体退相位噪声和集体旋转噪声的鲁棒量子对话(Quantum Dialogue, QD)协议. 在每个提出的QD协议中, 每个由4物理量子比特构成的4个逻辑Bell态被用于对抗集体噪声. 信息泄露问题通过从一个通信方向另一个通信方直接两步传送辅助逻辑Bell态来克服. Bell态测量而非4量子比特联合测量被用于解码. 抵抗窃听者主动攻击(如截获-重发攻击、测量-重发攻击、纠缠-测量攻击和木马攻击)的有效性能够得到保证.

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国家自然科学基金资助项目(61402407)

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表1 集体退相位噪声下4个逻辑Bell态之间的映射关系

	$\| Φ_{d p}^{+} ?$	$\| Φ_{d p}^{?} ?$	$\| Ψ_{d p}^{+} ?$	$\| Ψ_{d p}^{?} ?$
$Ω_{I}$	$\| Φ_{d p}^{+} ?$	$\| Φ_{d p}^{?} ?$	$\| Ψ_{d p}^{+} ?$	$\| Ψ_{d p}^{?} ?$
$Ω_{z}$	$\| Φ_{d p}^{?} ?$	$\| Φ_{d p}^{+} ?$	$\| Ψ_{d p}^{?} ?$	$\| Ψ_{d p}^{+} ?$
$Ω_{x}$	$\| Ψ_{d p}^{+} ?$	$\| Ψ_{d p}^{?} ?$	$\| Φ_{d p}^{+} ?$	$\| Φ_{d p}^{?} ?$
$Ω_{y}$	$\| Ψ_{d p}^{?} ?$	$\| Ψ_{d p}^{+} ?$	$\| Φ_{d p}^{?} ?$	$\| Φ_{d p}^{+} ?$

表2 集体旋转噪声下4个逻辑Bell态之间的映射关系

	$\| Φ_{r}^{+} ?$	$\| Φ_{r}^{?} ?$	$\| Ψ_{r}^{+} ?$	$\| Ψ_{r}^{?} ?$
$Θ_{I}$	$\| Φ_{r}^{+} ?$	$\| Φ_{r}^{?} ?$	$\| Ψ_{r}^{+} ?$	$\| Ψ_{r}^{?} ?$
$Θ_{z}$	$\| Φ_{r}^{?} ?$	$\| Φ_{r}^{+} ?$	$\| Ψ_{r}^{?} ?$	$\| Ψ_{r}^{+} ?$
$Θ_{x}$	$\| Ψ_{r}^{+} ?$	$\| Ψ_{r}^{?} ?$	$\| Φ_{r}^{+} ?$	$\| Φ_{r}^{?} ?$
$Θ_{y}$	$\| Ψ_{r}^{?} ?$	$\| Ψ_{r}^{+} ?$	$\| Φ_{r}^{?} ?$	$\| Φ_{r}^{+} ?$

表3 与之前的抗集体噪声的无信息泄露协议的对比

	文献[57]的协议	文献[58]的协议	本文提出的QD协议
初始量子资源	2个Bell态的乘积态	逻辑量子比特	逻辑Bell态
量子测量	Bell态测量	单粒子测量	Bell态测量
信息论效率	40%	33.3%	40%
量子信道容量	每轮2比特	每轮2比特	每轮4比特

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03.67.Dd	Quantum cryptography and communication security
03.67.Hk	Quantum communication
03.67.Pp	Quantum error correction and other methods for protection against decoherence (see also 03.65.Yz Decoherence; open systems; quantum statistical methods; for decoherence in Bose-Einstein condensates, see 03.75.Gg

	$\| Φ_{d p}^{+} ?$	$\| Φ_{d p}^{?} ?$	$\| Ψ_{d p}^{+} ?$	$\| Ψ_{d p}^{?} ?$
$Ω_{I}$	$\| Φ_{d p}^{+} ?$	$\| Φ_{d p}^{?} ?$	$\| Ψ_{d p}^{+} ?$	$\| Ψ_{d p}^{?} ?$
$Ω_{z}$	$\| Φ_{d p}^{?} ?$	$\| Φ_{d p}^{+} ?$	$\| Ψ_{d p}^{?} ?$	$\| Ψ_{d p}^{+} ?$
$Ω_{x}$	$\| Ψ_{d p}^{+} ?$	$\| Ψ_{d p}^{?} ?$	$\| Φ_{d p}^{+} ?$	$\| Φ_{d p}^{?} ?$
$Ω_{y}$	$\| Ψ_{d p}^{?} ?$	$\| Ψ_{d p}^{+} ?$	$\| Φ_{d p}^{?} ?$	$\| Φ_{d p}^{+} ?$

	$\| Φ_{r}^{+} ?$	$\| Φ_{r}^{?} ?$	$\| Ψ_{r}^{+} ?$	$\| Ψ_{r}^{?} ?$
$Θ_{I}$	$\| Φ_{r}^{+} ?$	$\| Φ_{r}^{?} ?$	$\| Ψ_{r}^{+} ?$	$\| Ψ_{r}^{?} ?$
$Θ_{z}$	$\| Φ_{r}^{?} ?$	$\| Φ_{r}^{+} ?$	$\| Ψ_{r}^{?} ?$	$\| Ψ_{r}^{+} ?$
$Θ_{x}$	$\| Ψ_{r}^{+} ?$	$\| Ψ_{r}^{?} ?$	$\| Φ_{r}^{+} ?$	$\| Φ_{r}^{?} ?$
$Θ_{y}$	$\| Ψ_{r}^{?} ?$	$\| Ψ_{r}^{+} ?$	$\| Φ_{r}^{?} ?$	$\| Φ_{r}^{+} ?$

Robust quantum dialogue based on a shared auxiliary logical Bell state against collective noise

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