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中国物理学会期刊

基于广义等距张量的压缩多光子纠缠态量子密钥分发

CSTR: 32037.14.aps.72.20230589

Generalized isometric tensor based quantum key distribution protocols of squeezed multiphoton entangled states

CSTR: 32037.14.aps.72.20230589
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  • 等距张量(即张量 \boldsymbol\omega 满足 \boldsymbol\omega ^\dagger \boldsymbol\omega = \boldsymbolI )为实现张量网络态(tensor network states, TNSs)中确定纠缠态的压缩提供了一种新颖而强大的数学构造算法. 结合等距张量, 本文发现在量子密钥分发(quantum key distribution, QKD)中可能采取完全不同的密钥生成方法, 即在不改变纠缠态结构和性质的情况下, 将任意多光子纠缠态压缩成单光子态或者Bell态. 在提出的QKD协议中, 输入态由任意纠缠态组成, 这些输入态首先被发送方Alice压缩成单光子态 \left| 0 \right\rangle \left| 1 \right\rangle 或Bell态, 使得提出的协议同时达到了多模存储和确定性传输的要求, 且减少了需要传输和存储的量子比特数量, 从而提高了QKD协议的编码能力. 然后再添加诱骗态在这些单光子态 \left| 0 \right\rangle \left| 1 \right\rangle 中, 再通过量子信道一起发送给接收方Bob, 以制备密钥. 最后, Alice和Bob利用筛选出来的压缩态|0\rangle 和|1\rangle 以及他们对应的等距张量的共轭转置来协商出共享密钥. 本文提出的协议比一般协议中的单光子能编码更多的经典比特, 显著提高了编码效率, 减少了量子资源的使用. 本文提出的QKD协议还保持了生成密钥的完美安全性.

     

    Isometric tensor offers a novel and powerful tool that can compress an entangled state into its tensor network state (TNS). The resulting quantum compression provides a new opportunity for enhancing quantum key distribution (QKD) protocols. The main idea explored in this work is to use the quantum compression to improve the efficiency of QKD. In a nut-shell, a collection of any multi-photon entangled states that carry encoded classical bits is compressed into a single-photon state before the corresponding photon is sent to the receiver that measures the qubit and decompresses it. In this paper, we first show how to obtain the generalized isometric tensors for compressing any entangled states and their inverse isometric tensors for decompression. In our proposed QKD protocol, the input state consists of any multi-photon entangled states, which are first compressed into a single-photon state \left| 0 \right\rangle or \left| 1 \right\rangle or Bell states by the sender Alice. A sequence of single-photon states \left| 0 \right\rangle and \left| 1 \right\rangle and one photon from the Bell state mixed with decoy qubits is sent to the receiver Bob via a quantum channel. Bob obtains the final sifted compressed states \left| 0 \right\rangle and \left| 1 \right\rangle and conjugate transpose of the isometric tensors. Using our protocols, Bob can decompress the received states \left| 0 \right\rangle and \left| 1 \right\rangle into original entangled states. Since quantum processors that are used to send quantum information between nodes are relatively primitive and low in power and the preparation of many-photon entanglement is relatively difficult at present, finding suitable protocols for the compression of transmitted quantum data brings important practical benefits. More generally, the quantum information theory primarily investigates quantum data manipulation under locality constraints, so our protocols connect naturally to these investigations. Our protocols increase the encoding capacity of QKD protocols. Not only our proposed processes of compression and decompression are very simple, but also entanglement compression using isometric tensors can be implemented by using quantum circuits and current technology. Because many ideas for designing of quantum information processing equipment envision that a network composed of relatively small quantum processors sending quantum information between nodes, it is greatly significant to find appropriate protocols for compressing the transmitted quantum data .

     

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