[0002] 量子密码，诞生于Bennett和Brassard在1984年提出的具有前瞻性的量子密钥分配(Quantumkey distribution，QKD)方法[1]，利用量子力学的性质而非数学问题的计算复杂性来达到无条件安全。量子密码已经吸引了许多注意力并确立许多有趣的分支，如QKD[1-5]、量子安全直接通信(Quantum secure direct communication，QSDC)[6-13]、量子秘密共享(Quantum secret sharing，QSS)[14-18]等。
[0003] QKD致力于利用量子信号的传送在两个远距离通信者之间建立一个随机密钥序列，而QSDC聚焦于将一个秘密消息从一个通信者直接传送到另一个通信者而无需事先建立一个随机密钥序列。在2004年，为了实现来自两个通信者的秘密消息的相互交换，Zhang和Man[19-20]以及Nguyen[21]分别独立提出量子对话(Quantum dialogue，QD)这一新概念。QD极大地激发起研究者们的兴趣。然而，早期的QD方法[19-27]总存在信息泄露问题，意味着任何其他人无需发起任何主动攻击就能轻易地提取到关于两个通信者秘密消息的一些有用信息。QD的信息泄露问题是被Gao等[28]以及Tan和Cai[29]在2008年分别独立发现。随后，研究者们迅速转向研究如何解决QD的信息泄露问题。到目前为止，许多优秀的方法已经被提出来，如辅助量子态的直接传送[30-37]、Bell态的提取相关性[38]、控制非操作和辅助单光子[39]、量子纠缠态纠缠交换产生的测量相关性[40-41]、量子纠缠态纠缠交换结果集合编码[34-36]、量子加密共享[42-43]、辅助量子操作[44]以及量子纠缠态的测量相关性[45]。
[0004] 在2007年，利用著名的BB84方法[1]，Boyer等[46]提出首个半量子密码方法(即BKM2007方法)，只允许一个通信者具备量子能力。在BKM2007方法中，接收者Bob被受限于在量子信道执行以下操作：(a)发送或不带干扰地返回量子比特；(b)用固定的正交基{|0>,|1>}测量量子比特；(c)制备(新的)量子比特处于固定的正交基{|0>,|1>}。在2009年，Boyer等[47]利用单光子构建了一个基于置乱的半量子密 钥分配 (Sem i-quantumkeydistribution，SQKD)方法，其中接收者Bob被受限于执行(a)、(b)和(d)(利用不同延迟线)重新排序量子比特。根据文献[46-47]方法的定义，正交基{|0>,|1>}可被视为经典基并用经典记号{0,1}代替，因为它只涉及量子比特|0>和|1>而非任何量子叠加态。而且，接收者Bob被受限于执行以上(a)、(b)、(c)和(d)四种操作，可被视为经典的。显然，不同于传统量子密码要求所有通信者都具备量子能力，半量子密码允许部分通信者具备经典能力而非量子能力以致于她们不需要涉及量子叠加态的制备和测量。因此，半量子密码有利于部分通信者减轻量子态制备和测量的负担。
[0005] 自从“半量子”的概念首次被Boyer等[46]提出，研究者们对它显示出极大的热情并尝试将它应用到不同的量子密码任务，如QKD、QSDC和QSS。这样，许多半量子密码方法，如SQKD方法[46-63]、半量子安全直接通信(Semi-quantumsecuredirectcommunication，SQSDC)方法[50,64]、半量子秘密共享(Semi-quantumsecretsharing，SQSS)方法[65-69]、半量子隐私比较(Semi-quantumprivate comparison，SQPC)方法[70-71]、半量子密钥协商(Semi-quantumkeyagreement，SQKA)方法[72-73]、受控确定性安全半量子通信(Controlled deterministic secure semi-quantum communication，CDSSQC)方法[73]、半量子对话(Semi-quantum dialogue，SQD)方法[73]等，被设计出来。
[0006] 容易发现，以上所有QD方法[19-27,30-45]要求两个通信者都具备量子能力。然而，这一要求可能是不切实际的，因为并不是两个通信者都能负担得起昂贵的量子资源和操作。如果只有一个通信者具备量子能力，那么对话能否成功进行？文献[73]利用Bell纠缠态提出的首个SQD方法给了这个问题一个肯定的回答。
[0007] 基于以上分析，本发明致力于利用单光子作为量子载体提出一种不要求经典通信者具备测量能力的SQD方法，实现一个量子通信者和一个经典通信者之间的双向通信。本发明方法相比于传统无信息泄露QD方法的优势在于它只要求一个通信者具备量子能力。与现有的SQD方法相比，本发明方法的优势在于它仅采用单光子而非两光子纠缠态作为量子载体。
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[0090] 本发明的目的是设计一种基于单光子的不要求经典通信者具备测量能力的半量子对话方法，实现一个量子通信者和一个经典通信者之间的双向通信。
[0091] 一种基于单光子的不要求经典通信者具备测量能力的半量子对话方法，共包括以下七个过程：
[0092] S1)量子Alice制备N个随机处于四个量子态{|0>,|1>,|+>,|->}之一的单光子并将它们通过块传输的方式[6]传送给经典Bob，其中 和N为自然数。
[0093] S2)为了编码他自己的秘密消息，Bob制备2N个信息单光子处于Z基，其中Z基为正交基{0>,|1>}：如果他的秘密经典比特是0，他制备两个相邻的信息单光子处于相同的状态；如果他的秘密经典比特是1，他制备两个相邻的信息单光子处于相反的状态。而且，Bob制备M+2N(M≥N)个样本单光子随机处于Z基，其中M为自然数。Bob选出2N个样本单光子，利用它们与2N个信息单光子一起构成一个量子比特序列 在收到来自Alice的N个单光子后，Bob利用它们与剩余的M个样本单光子一起构成一个量子比特序列|φ>。然后，Bob随机从量子比特序列|φ>中选出2N个单光子|ψ>。最后，Bob将 和|ψ>中的单光子一起重新排序并通过块传输的方式[6]发送给Alice。为方便起见，在|ψ>中，称来自Alice的单光子为CTRL单光子，Bob制备的单光子为SIFT单光子。
[0094] S3)Bob公布属于|ψ>的单光子的位置。Alice随机用Z基或X基测量|ψ>中的每个单光子，其中X基为正交>{|+>,|->}。
[0095] S4)Bob公布|ψ>中单光子的顺序。与此同时，Alice公布|ψ>中她用Z基测量的位置。Z-SIFT比特代表Alice用Z基测量STFT单光子所产生的比特。
[0096] S5)Alice通过比较她的测量结果和她制备的量子态来检查|ψ>中CTRL单光子的错误率。如果Alice在步骤S3选择正确的基测量|ψ>中的CTRL单光子，那么她的测量结果应当与她制备的量子态一样。如果错误率高于某个预定的阈值PCTRL，她们终止通信。
[0097] S6)Alice公布|ψ>中Z-SIFT比特的值。Alice的测量结果应当与Bob制备的量子态一样。Bob检查|ψ>中Z-SIFT比特的错误率。如果错误率高于某个预定的阈值PZ-SIFT，她们终止通信。
[0098] S7)Alice丢弃属于|ψ>的单光子。Bob公布 中的2N个信息单光子的位置和顺序。在Bob宣布它们后，Alice丢弃 中的2N个样本单光子并将剩余的2N个信息单光子恢复到原始顺序。然后Alice测量每两个相邻信息单光子以读出Bob的秘密消息。具体地，如果Alice测得每两个相邻信息单光子处于相同的量子态，那么Alice就知道Bob的秘密经典比特是0；如果Alice测得每两个相邻信息单光子处于相反的量子态，那么Alice就知道Bob的秘密经典比特是1。为了将她的秘密消息传送给Bob，Alice根据以下规则执行经典一次一密加密过程并将密文向Bob宣布：如果她测得每两个相邻信息单光子的第二个光子处于量子态|0>以及她的秘密经典比特是0，她向Bob宣布0；如果她测得每两个相邻信息单光子的第二个光子处于量子态|0>以及她的秘密经典比特是1，她向Bob宣布1；如果她测得每两个相邻信息单光子的第二个光子处于量子态|1>以及她的秘密经典比特是0，她向Bob宣布1；如果她测得每两个相邻信息单光子的第二个光子处于量子态|1>以及她的秘密经典比特是1，她向Bob宣布0。根据Alice宣布的密文和他自己制备的所有的每两个相邻信息单光子的第二个光子所代表的经典比特，Bob能直接解密出Alice的秘密消息。
