【作者】 闫凤利；

【导师】 李有成；

【作者基本信息】 河北师范大学 ， 凝聚态物理， 2008， 博士

【摘要】 1.量子秘密共享我们提出了一个用4个量子态实现的多方与多方之间的量子秘密共享方案,并证明此方案对用多光子信号的特洛伊马攻击,用Einstein-Podolsky-Rosen对的伪信号攻击,单光子攻击,以及不可见光子攻击是安全的。另外,给出了不忠实者使用任意两粒子纠缠态伪信号攻击方法窃听秘密信息平均成功概率的上界。接着,我们又提出了一个用6个量子态实现的多方(一组的m个成员)与多方(二组的n个成员)之间的量子秘密共享方案。在这个量子密钥共享协议中,一组的所有成员通过幺正操作将他们各自的秘密直接编码在单光子态上,然后最后一人(一组的第m个成员)把最后所得到的量子位平均分成n份,并将这n份分别发送给二组的n个成员。通过测量对应的量子位,由一组的m个成员共享的秘密信息也被二组的n个成员共享。此方案的特征是每个组的任何部分成员或一组的部分成员和二组的部分成员的联合都不能读出秘密,只有每个组的全体成员一起才可以得到秘密。此协议的效率近似100%。此方案使多光子信号的特洛伊马攻击, Einstein-Podolsky-Rosen对的伪信号攻击,单光子攻击,以及不可见光子攻击无效。此协议比用4个量子态实现的多方与多方之间的量子秘密共享方案优越。我们也给出了不忠实者使用任意两粒子纠缠态伪信号攻击方法窃听秘密信息平均成功概率的上界。我们还提出了仅用单光子和幺正操作在Alice组和Bob组之间实现秘密共享的另一个方案。在此方案中,Alice组的一个成员准备处于4个不同态的单光子序列,其他成员则在这个单光子序列上用幺正操作编码各自的量子信息。之后Alice组的最后一个成员将这组编码好的单光子序列发送给Bob组。Bob组除最后一个成员外,其他成员作同Alice组成员类似的工作,而Bob组的最后一个成员测量这些量子位。通过一些检验,如果通信者能确认量子通道是安全的,则Alice组的最后一个成员所送的量子位就是两组之间共享的秘密。2.控制的量子隐形传态我们研究了使用一般的三量子位态作为量子通道成功控制传输一个未知量子态的概率。给出了经由各种包括Greenberger-Horne-Zeilinger态和W态在内的三量子位态作为量子通道成功控制传输一个未知量子态的最大概率的解析表示。除此之外我们还确定了另一种局域纠缠。进一步地我们得到了通过测量一个量子位使三量子位态塌缩成Einstein-Podolsky-Rosen对的充分必要条件,并找出了能以单位概率和单位忠实度控制传输未知量子态的三量子位态量子通道的集合。3.一个正算子测量的实现我们给出了实现一个正算子测量的幺正变换的矩阵分解,从而使这一正算子测量能用基本的量子逻辑门,和对辅助量子位的测量来实现。应用这个正算子测量可实现一个未知两量子位态的概率隐形传输。4.通信中心和其他M个成员之间进行同时的量子安全直接通信的容量我们分析了使用M +1粒子Greenberger-Horne-Zeilinger态作为量子通道,采用交换纠缠方法,通信中心和其他M个成员之间进行同时的量子安全直接通信的容量。证明了如果其他M个成员想传输M + 1位经典信息给通信中心,则编码方案应该是秘密的。然而,我们证明当编码方案公开时,无论M多大,此同时的安全直接通信方案只能传送2位的经典信息。更多还原

【Abstract】 1. Quantum secret sharingA protocol of quantum secret sharing between multiparty and multiparty with four states ispresented. We show that this protocol can make the Trojan horse attack with a multi-photonsignal, the fake-signal attack with Einstein-Podolsky-Rosen pairs, the attack with single photons,and the attack with invisible photons to be nullification. In addition, we also give the upperbounds of the average success probabilities for dishonest agent eavesdropping encryption usingthe fake-signal attack with any two-particle entangled states.We also propose a quantum secret sharing scheme between m-party and n-party using threeconjugate bases, i.e. six states. A sequence of single photons, each of which is prepared in oneof the six states, is used directly to encode classical information in the quantum secret sharingprocess. In this scheme, each of all m members in group 1 choose randomly their own secret keyindividually and independently, and then directly encode their respective secret information onthe states of single photons via unitary operations, then the last one (the mth member of group1) sends 1/n of the resulting qubits to each of group 2. By measuring their respective qubits,all members in group 2 share the secret information shared by all members in group 1. Thesecret message shared by group 1 and group 2 in such a way that neither subset of each groupnor the union of a subset of group 1 and a subset of group 2 can extract the secret message, buteach whole group (all the members of each group) can. The scheme is asymptotically 100% ine?ciency. It makes the Trojan horse attack with a multi-photon signal, the fake-signal attackwith Einstein-Podolsky-Rosen pairs, the attack with single photons, and the attack with invisiblephotons to be nullification. We show that it is secure and has an advantage over the one basedon two conjugate bases. We also give the upper bounds of the average success probabilitiesfor dishonest agent eavesdropping encryption using the fake-signal attack with any two-particleentangled states. This protocol is feasible with present-day technique.Another scheme of quantum secret sharing between Alices’group and Bobs’group withsingle photons and unitary transformations has been put forward. In the protocol, one memberin Alices’group prepares a sequence of single photons in one of four di?erent states, whileother members directly encode their information on the sequence of single photons via unitaryoperations, after that the last member sends the sequence of single photons to Bobs’group. ThenBobs except for the last one do work similarly. Finally last member in Bobs’group measures the qubits. If Alices and Bobs guaranteed the security of quantum channel by some tests, thenthe qubit states sent by last member of Alices’group can be used as key bits for secret sharing.It is shown that this scheme is safe.2. Controlled teleportationThe probability of successfully controlled teleporting an unknown qubit using a generalthree-particle state is investigated. We give the analytic expressions of maximal probabilitiesof successfully controlled teleporting an unknown qubit via every kinds of tripartite states in-cluding a tripartite Greenberger-Horne-Zeilinger state and a tripartite W-state, respectively.Besides, another kind of localizable entanglement is also determined. Furthermore, we obtainthe su?cient and necessary condition that a three-qubit state can be collapsed to an Einstein-Podolsky-Rosen pair by a measurement on one qubit, and characterize the three-qubit statesthat can be used as quantum channel for controlled teleporting a qubit of unknown informationwith unit probability 1 and with unit fidelity.3. An implementation of a positive operator valued measureAn implementation of the positive operator valued measure (POVM) is given. In particular,we give a decomposition of the unitary operation which plays an important role in the imple-mentation of the positive operator valued measure. By using this POVM one can realize theprobabilistic teleportation of an unknown two-particle state.4. Capacity of a simultaneous quantum secure direct communication schemebetween the central party and other M partiesWe analyze the capacity of a simultaneous quantum secure direct communication schemebetween the central party and other M parties via M + 1-particle Greenberger-Horne-Zeilingerstates and swapping quantum entanglement. It is shown that the encoding scheme should besecret if other M parties wants to transmit M + 1 bit classical messages to the center partysecretly. However when the encoding scheme is announced publicly, we prove that the capacityof the scheme in transmitting the secret messages is 2 bits, no matter how M is.更多还原