量子密码通信若干问题的研究
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摘要
量子通信和量子密码学是传统密码学和量子力学相结合的产物,为信息的安全传输提供了一种全新的方法。不同于以数学问题为基础的传统密码体制,量子密码学的安全性是由海森堡测不准原理以及单量子不可克隆定理来保证的。量子密码学不仅具有可证明的安全性,而且具有窃听者存在的可检测性,这是其他密码体制所不具备的特性,具有重要的应用前景和深远的意义。
本文主要探讨和研究量子密码通信中量子密钥分发、量子秘密共享、量子受控传输以及量子安全直接通信等方面的一些问题,本文所做的工作如下:
第一,提出了一个基于欧洲Secoqc QKD网络结构的量子密钥分配协议。基于纠缠交换,并采用随机空间量子信道选择,提高了安全性。特点有:适用于网状网络,使用较少的量子资源,并且只需要少量的比特检测是否有Eve窃听。
第二,提出了一个基于纠缠交换和随机EPR选择的多方量子共享协议。发送方可以随机选择EPR对进行Bell基测量,这样可以提高方案的安全性,此外,还采用差分编码来获得较高的效率,并且该过程需要的量子资源较少。
第三,提出了一种基于Bell态纠缠变换的远程受控传输多qudit量子态的机制。其控制参数通过最大纠缠d维EPR对的纠缠变换得到。该方案是高维受控传输协议,具有更高的编码容量和更好的安全性。
第四,提出了一个基于GHZ受控传输的高维多方量子安全直接通信方案。采用随机选择Z基或X基测量,以及插入诱骗光子的方法保证了量子信道安全性,通过d维Bell基测量和对应的Z基或X基测量实现秘密信息的安全通信。
第五,提出了一种EPR与GHZ相结合的非纠缠信道下传输W态的方案。GHZ态不仅作为控制参数,而且还作为量子信道。成功传输的总概率只与信道条件有关,而与控制方的个数无关。并将其扩展到混合信道下对任意n-qubit的量子受控传输。第六,提出了采用非最大纠缠d维GHZ作为量子信道时受控传输n-qudit
态的一个通用方案。以传输成功率小于1的代价实现保真度为1传输任意n-qudit态。给出了传输成功率的表达式,它取决于量子信道和广义Bell基的匹配程度,还给出了用来恢复原始状态的幺正操作的解析表达式。最后将本方案扩展到EPR和GHZ混合信道,进一步减少了量子资源的开销。
Quantum communication and quantum cryptography is a subject which combines traditional cryptography and quantum mechanics. It provides an optional new method for information security. Different from traditional cryptography which based on the assumed difficulty of mathematical problems, the security of quantum cryptography is based on Heisenberg uncertainty principle and quantum no-cloning theorem. Quantum cryptography not only has proven security and also can be detected if eavesdropping has occurred. Compared with other cryptography schemes, these are specific characteristic, which has an important application prospect and far-reaching significance.
In this thesis, some questions of the quantum cryptography communication have been explored and studied, such as quantum key distribution, quantum secret sharing, quantum controlled teleportation, quantum secure direct communication and so on. The main works done are listed as follows.
First, according to the structure of European Secoqc QKD network, a quantum key distribution protocol is proposed based on entanglement swapping, and random space quantum channel selection to improve the probability of revealing Eve. The protocol proposed exhibits the following features. It is proper to mesh QKD network structure. And it can be generated using the less quantum resource. Detecting Eve requires the comparison of fewer bits.
Secondly, a multi-party quantum state sharing protocol is suggested by using entanglement swapping and random EPR selection. The EPR pairs of Bell-state measurement are selected randomly by the sender which can improve the security of the scheme and raise probability of detecting Eve. In addition, difference coding is used in this protocol to achieve a high efficiency. It is convenient in application as it require less quantum resource.
Third, a scheme for teleporting multi-qudit quantum state is presented, via many controllers, based on Bell-state entanglement swapping. The presented scheme is the qudit case of controlled teleportation protocol, whose control parameters are obtained using entanglement swapping of maximally d-dimensional EPR pair. The scheme of multi-qudit owns the advantage of having higher code capacity and better security than that of multi-qutrit or multi-qubit.
Four, a multiparty controlled secure quantum communication of d-dimensional is proposed based on GHZ state and teleportation. After using decoy photons to check eavesdropping efficiently for the purpose of the quantum channel security, the sender encodes the secret message of d-dimensional on a sequence of additional particle states and then fulfills teleportation of the secret through d-dimensional Bell state measurement and X-basis or Z-basis measurement.
Five, a scheme for probabilistic controlled teleportation of a triplet W state using combined non-maximally entangled channel of EPR and GHZ is given. In this scheme, the GHZ state serves not only as the control parameter but also as quantum channel. The total probability of successful teleportation is only dependent on channel coefficients of EPRs and GHZ, independent of the number of supervisors. And it is extended to the arbitrary n-qubit quantum controlled transmission using the mixed-channel.
Six, we explicitly present a general scheme for controlled quantum teleportation of an arbitrary multi-qudit state with unit fidelity and non-unit successful probability using d-dimensional nonmaximally entangled GHZ states as the quantum channel and generalized d-dimensional Bell states as the measurement basis. The expression of successful probability for controlled teleportation is present depending on the degree of entanglement matching between the quantum channel and the generalized Bell states. And the formulae for the selection of operations performed by the receiver are given according to the results measured by the sender and the controller. Finally, the scheme is extended to the mixed EPR and GHZ channel to further reduce the quantum of resources costs.
本文主要探讨和研究量子密码通信中量子密钥分发、量子秘密共享、量子受控传输以及量子安全直接通信等方面的一些问题,本文所做的工作如下:
第一,提出了一个基于欧洲Secoqc QKD网络结构的量子密钥分配协议。基于纠缠交换,并采用随机空间量子信道选择,提高了安全性。特点有:适用于网状网络,使用较少的量子资源,并且只需要少量的比特检测是否有Eve窃听。
第二,提出了一个基于纠缠交换和随机EPR选择的多方量子共享协议。发送方可以随机选择EPR对进行Bell基测量,这样可以提高方案的安全性,此外,还采用差分编码来获得较高的效率,并且该过程需要的量子资源较少。
第三,提出了一种基于Bell态纠缠变换的远程受控传输多qudit量子态的机制。其控制参数通过最大纠缠d维EPR对的纠缠变换得到。该方案是高维受控传输协议,具有更高的编码容量和更好的安全性。
第四,提出了一个基于GHZ受控传输的高维多方量子安全直接通信方案。采用随机选择Z基或X基测量,以及插入诱骗光子的方法保证了量子信道安全性,通过d维Bell基测量和对应的Z基或X基测量实现秘密信息的安全通信。
第五,提出了一种EPR与GHZ相结合的非纠缠信道下传输W态的方案。GHZ态不仅作为控制参数,而且还作为量子信道。成功传输的总概率只与信道条件有关,而与控制方的个数无关。并将其扩展到混合信道下对任意n-qubit的量子受控传输。第六,提出了采用非最大纠缠d维GHZ作为量子信道时受控传输n-qudit
态的一个通用方案。以传输成功率小于1的代价实现保真度为1传输任意n-qudit态。给出了传输成功率的表达式,它取决于量子信道和广义Bell基的匹配程度,还给出了用来恢复原始状态的幺正操作的解析表达式。最后将本方案扩展到EPR和GHZ混合信道,进一步减少了量子资源的开销。
Quantum communication and quantum cryptography is a subject which combines traditional cryptography and quantum mechanics. It provides an optional new method for information security. Different from traditional cryptography which based on the assumed difficulty of mathematical problems, the security of quantum cryptography is based on Heisenberg uncertainty principle and quantum no-cloning theorem. Quantum cryptography not only has proven security and also can be detected if eavesdropping has occurred. Compared with other cryptography schemes, these are specific characteristic, which has an important application prospect and far-reaching significance.
In this thesis, some questions of the quantum cryptography communication have been explored and studied, such as quantum key distribution, quantum secret sharing, quantum controlled teleportation, quantum secure direct communication and so on. The main works done are listed as follows.
First, according to the structure of European Secoqc QKD network, a quantum key distribution protocol is proposed based on entanglement swapping, and random space quantum channel selection to improve the probability of revealing Eve. The protocol proposed exhibits the following features. It is proper to mesh QKD network structure. And it can be generated using the less quantum resource. Detecting Eve requires the comparison of fewer bits.
Secondly, a multi-party quantum state sharing protocol is suggested by using entanglement swapping and random EPR selection. The EPR pairs of Bell-state measurement are selected randomly by the sender which can improve the security of the scheme and raise probability of detecting Eve. In addition, difference coding is used in this protocol to achieve a high efficiency. It is convenient in application as it require less quantum resource.
Third, a scheme for teleporting multi-qudit quantum state is presented, via many controllers, based on Bell-state entanglement swapping. The presented scheme is the qudit case of controlled teleportation protocol, whose control parameters are obtained using entanglement swapping of maximally d-dimensional EPR pair. The scheme of multi-qudit owns the advantage of having higher code capacity and better security than that of multi-qutrit or multi-qubit.
Four, a multiparty controlled secure quantum communication of d-dimensional is proposed based on GHZ state and teleportation. After using decoy photons to check eavesdropping efficiently for the purpose of the quantum channel security, the sender encodes the secret message of d-dimensional on a sequence of additional particle states and then fulfills teleportation of the secret through d-dimensional Bell state measurement and X-basis or Z-basis measurement.
Five, a scheme for probabilistic controlled teleportation of a triplet W state using combined non-maximally entangled channel of EPR and GHZ is given. In this scheme, the GHZ state serves not only as the control parameter but also as quantum channel. The total probability of successful teleportation is only dependent on channel coefficients of EPRs and GHZ, independent of the number of supervisors. And it is extended to the arbitrary n-qubit quantum controlled transmission using the mixed-channel.
Six, we explicitly present a general scheme for controlled quantum teleportation of an arbitrary multi-qudit state with unit fidelity and non-unit successful probability using d-dimensional nonmaximally entangled GHZ states as the quantum channel and generalized d-dimensional Bell states as the measurement basis. The expression of successful probability for controlled teleportation is present depending on the degree of entanglement matching between the quantum channel and the generalized Bell states. And the formulae for the selection of operations performed by the receiver are given according to the results measured by the sender and the controller. Finally, the scheme is extended to the mixed EPR and GHZ channel to further reduce the quantum of resources costs.
引文
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