International Journal of Quantum Information

In this thesis, we describe the one-way quantum computer , a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state. We prove the universality of the , describe the underlying computational model and demonstrate that the can be operated fault-tolerantly.

In Sec. 2, we show that the can be regarded as a simulator of quantum logic networks. In this way, we prove the universality and establish the link to the network model — the common model of quantum computation. We also indicate that the description of the as a network simulator is not adequate in every respect.

In Sec. 3, we derive the computational model underlying the , which is very different from the quantum logic network model. The has no quantum input, no quantum output and no quantum register, and the unitary gates from some universal set are not the elementary building blocks of quantum algorithms. Further, all information that is processed with the is the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The is nevertheless quantum-mechanical, as it uses a highly entangled cluster state as the central physical resource.

In Sec. 4, we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the . Further, we outline the concept of checksums in the context of the , which may become an element in future practical and adequate methods for fault-tolerant computation.

Zeng and Keitel proposed an arbitrated quantum signature scheme in 2002. Recently, Curty and Lütkenhaus pointed out that the protocol is not operationally specified. In a reply, Zeng gave more details of the scheme. The author also claimed that the scheme is suitable for unknown messages. In this letter, we remark that the invented scenario in the original scheme is artificial. This is because its security entirely depends on the presence of a trustworthy arbitrator. Moreover, the claim that the original scheme is suitable for unknown messages is not sound.

We construct a generalized controlled phased gate entangler for a multi-qubit state based on the geometrical structure of quantum systems. We also investigate the relation between the generalized controlled phase construction of a quantum gate entangler and graph state for two-qubit and three-qubit states.

Quantum Key Distribution (QKD) networks are the trends toward multiple users' unconditional secure communication. Based on several passive optical devices, such as beam splitter, optical switch or wavelength divided multiplexer, various types of fiber-based QKD networks have been proposed. However, it is still hard to accurately assess these networks. To find the optimal solution, a general assessment that would not involve detailed schemes is quite necessary. In this paper, we introduce an evaluation method and analyze optical-device-based QKD networks including two rational aspects: (i) network connectivity and network bandwidth which reflect the network's flexibility and performance in theory; (ii) network cost that brings pragmatic restriction on the network construction in practice. Applying this model, we compare five typical types of optical-device-based QKD networks. The explicit results demonstrate the above networks' characteristics and some valuable conclusions.

We experimentally demonstrate a protocol of probabilistic remote state preparation by virtue of entanglement, local operation and forward classical communications. Arbitrary polarization qubit state can be remotely prepared with this protocol. For both pure states and mixed states, the average efficiency is no less than 50% and the classical information cost is 1 bit. All 18 remotely prepared states were estimated with quantum state tomography system. The fidelities are all above 0.99, with average fidelity being 0.9956.

Two schemes for controlled dense coding with a extended GHZ state are investigated. In these protocols, the supervisor (Cliff) can control the average amount of information transmitted from the sender (Alice) to the receiver (Bob) only by adjusting his local measurement angle θ. It is shown that the results for the average amounts of information are unique from the different two schemes.

We propose a (t, n)-threshold multiparty quantum-information splitting protocol following some ideas of the standard teleportation protocol [C. H. Bennett, G. Brassard, C. Crpeau, R. Jozsa, A. Peres and W. K. Wootters, Phys. Rev. Lett.70 (1993) 1895] and Tokunaga et al.'s protocol [Y. Tokunaga, T. Okamoto and N. Imoto, Phys. Rev. A71 (2005) 012314]. The sender distributes the classical shared keys to his or her n agents and each agent owns a secret key in advance. The sender's quantum information can be extracted by an agent subset by collaboration in such a way that at least t or more agents can get the quantum information with the mutual assistances but any t - 1 or fewer agents cannot. In contrast to the previous multiparty quantum-information splitting protocols in which the sender's quantum information can be recovered only if all the agents collaborate, our protocol is more practical and more flexible.

We consider a one-dimensional array of superconducting transmission line resonators (TLRs). The TLRs are coupled by current-biased Josephson junctions, which act as tunable couplers between each two nearest TLRs, and a superconducting qubit is fabricated in the center of each TLR. We show that some important quantum information processing, such as quantum state transfer and preparation of remote entanglement, can be achieved in this system, and we also propose a scheme for generating the W-class states.

We investigate the phase matching problem in the fixed-point quantum search algorithm proposed by Grover [Phys. Rev. Lett.95 (2005) 150501]. We show that the optimal phase shift is π/3.61, which replaces the π/3 phase shift in fixed-point quantum search algorithm. The π/3.61-phase algorithm can be achieved in with the success probability of at least 94.11%, which offsets disadvantage that the success probability of getting correct results usually decreases with the increase of marked items when original Grover quantum search algorithm is applied to search an unordered database. In the meantime, this work also indicates that Grover quantum search algorithm is considerably robust to certain kinds of perturbations and is robust against modest noise in the initialization procedure.

A new method to obtain self-orthogonal codes over finite field F₂ is presented. Based on this method, we provide a construction for quantum error-correcting codes starting from cyclic codes over finite ring R = F₂ + uF₂. As an example, we present infinite families of quantum error-correcting codes which are derived from cyclic codes over the ring R = F₂ + uF₂.

A method of constructing Temperley-Lieb algebra (TLA) representations has been introduced in [Xue et al. arXiv:0903.3711]. Using this method, we can obtain another series of n² × n² matrices U which satisfy the TLA with the single loop . Specifically, we present a 9 × 9 matrix U with . Via Yang-Baxterization approach, we obtain a unitary -matrix, a solution of the Yang-Baxter equation. This 9 × 9 Yang-Baxter matrix is universal for quantum computing.

The secure quantum sealed-bid auction protocol [Mosayeb Naseri, Opt. Commun.282 (2009) 1939] is revisited. It is found that, utilizing intercept-measure-resend attacks, any evil bidder can make the auction aborted without being detected by the auctioneer. Further, if the evil bidder succeeds to be the first bidder, then he/she can win conclusively in the auction. To prevent such attacks, some defence strategies are adopted in the qubit distribution stage and the channel security check stage respectively and the original protocol is therefore modified somewhat.