多跳噪声量子纠缠信道特性及最佳中继协议

Characteristics of multi-hop noisy quantum entanglement channel and optimal relay protocol

在量子通信网络中,最佳中继路径的计算与选择策略是影响网络性能的关键因素.针对噪声背景下量子隐形传态网络中的中继路径选择问题,本文首先研究了相位阻尼信道及振幅阻尼信道上的纠缠交换过程,通过理论推导给出了两种多跳纠缠交换信道上的纠缠保真度与路径等效阻尼系数.在此基础上提出以路径等效阻尼系数为准则的隐形传态网络最佳中继协议,并给出了邻居发现、量子链路噪声参数测量、量子链路状态信息传递、中继路径计算与纠缠资源预留等工作的具体过程.理论分析与性能仿真结果表明,相比于现有的量子网络路径选择策略,本文方法能获得更小的路径平均等效阻尼系数及更高的隐形传态保真度.此外,通过分析链路纠缠资源数量对协议性能的影响,说明在进行量子通信网设计时,可以根据网络的规模及用户的需求合理配置链路纠缠资源.

The optimal relay path calculation and selection are important factors to affect the performance of quantum communication network. Current researches seldom consider the quantum path selection in real noisy environments.One of the difficult problems is how to analyze the influence of the noise on the quantum communication in multihop channels. This paper aims to solve the path selection problem of the quantum teleportation network in noisy environments. The process of entanglement swapping in the phase damping channel is first studied with an example of two-hop quantum channel, whose damping factors are p_1 and p_2. The entanglement states Φ~＋_（12）and Φ~_（＋34） are distributed separately in each hop. After the entanglement swapping, the density matrix of the entanglement state of photon 1 and photon 4 is obtained by performing a partial trace over the environment. Then, the Bures fidelity of this entanglement is calculated. After that, we define the path equivalent damping factor to describe the characteristic of the two-hop noisy quantum relay path. With an equivalent calculation method, the results above can be generalized to multi-hop channel.The path equivalent damping factor of the multi-hop amplitude damping channel is also obtained. According to these results, we propose an optimal relay protocol for the quantum teleportation network with the criterion of path equivalent damping factor, which means that a relay path with the minimum path equivalent damping factor can obtain the highest teleportation fidelity. The types and parameters of the messages used in the protocol are given. The processes of the relay protocol are described specifically, including neighbor finding, quantum link noise measurement, and quantum link status transmission. An improved Dijkstra algorithm is used in the optimal path calculation. Furthermore, because the entanglement resources maintained in the quantum nodes are limited and may be exhausted in superior quantum links,we propose a resource reservation method to avoid the failure of the relay path setup. Theoretical analysis and simulation show that our method can obtain a lower average equivalent damping factor and higher teleportation fidelity. It can also be seen that increasing the number of the entanglement resources will raise the performance of the quantum network,however, it brings higher cost and complexity. Therefore, the entanglement resources maintained in the quantum nodes must be configured reasonably according to the network scale, the cost, the time delay and the need of the users.