多方计算问题及光场相干态信号量子检测的研究

发布时间：2019-05-19 23:26

【摘要】：在量子通信复杂度的相关研究中,任意多方计算模型的通信复杂度研究越来越受到人们的关注。在光场相干态信号的量子检测方面,最小差错区分(MED)测量的研究已有较好的结果,而相干态非含糊状态区分(USD)的研究工作正在逐渐展开。本文就此进行分析和研究,其主要创新性成果如下:(1)从多方约会(MPD)问题的经典通信复杂度入手,研究MPD问题的量子分布式算法,给出MPD问题的量子通信复杂度,证明了其量子通信复杂度与经典情况相比最多有接近二次多项式级的降低。分析结果验证了量子算法的性能优势,尤其当用户数很大时,这种优势将更加明显。(2)研究基于通用判别函数的多方计算(MPC)问题的经典通信复杂度,给出该问题的量子分布式算法和量子通信复杂度。研究结果表明,量子算法的性能主要取决于函数定义域的平方根与用户数之间的无穷大阶的差距。量子通信复杂度较之经典情形最多将会有接近二次多项式级的降低。(3)研究基于判别函数的MPC问题和MPD问题的“解”数量估计,给出相应的“解”数量估计算法。研究结果表明:对于MPC问题,使用量子相位估计算法估计“解”的数量,其量子通信复杂度与量子分布式算法相当;对于MPD问题,无需任何多方通信就能够以近似相位估计算法的效能估算出“解”的数量。仿真实验验证了其有效性。(4)研究OOK调制相干态信号的USD测量,给出它在热噪声场背景下的确定性概率和差错概率的解析表达式。利用相干态的对称性,进一步研究了BPSK调制和QPSK调制下的相干态信号的USD测量,分别给出它们在热噪声场背景下确定性概率和差错概率的解析表达式。研究结果表明,热噪声场的存在使得最优USD测量退化成一般量子测量,因此在实际中实现理想USD测量是不可能的,且热噪声场的平均光子数大小决定了USD测量偏离理想状况的程度。(5)研究基于对称相干态的多址接入信道模型,给出其平均用户间干扰的解析表达式。在此模型的基础上,研究基于USD测量的多用户检测方法,给出用户间检测差错概率的解析表达式。研究结果表明,较之采用MED测量出现差错的情况,采用理想USD测量可以无差错地区分不同用户。(6)研究基于对称相干态的二址接入信道模型。在此模型的基础上,分别给出基于MED测量和USD测量的用户间检测差错概率以及最大信道容量的解析表达式。研究表明,采用USD测量可以无差错地区分不同用户,但是最大信道容量却比采用MED测量来得小。此外,还给出热噪声场背景下采用USD测量的用户间检测差错概率以及最大信道容量的解析表达式。研究表明,随着热噪声场平均光子数从0开始逐渐增高,采用USD测量的用户检测差错概率将从无差错开始逐步增大,最大信道容量将从无噪声情况开始逐步减小。针对MPD和MPC等问题的研究结果表明,采用量子分布式算法能够有效地降低多方通信开销。含噪相干态USD测量的研究丰富了相干态信号量子检测的内容,并且采用USD测量的量子多用户检测的效能优于MED方式。这些成果对光量子通信技术的进一步研究,具有理论意义和应用参考价值。
[Abstract]:In the related research of the quantum communication complexity, the research on the communication complexity of any multi-party computing model is more and more concerned. In terms of the quantum detection of the coherent state signal of the light field, the research of the minimum error distinguishing (MED) measurement has better results, and the research work of the coherent state non-ambiguity state discrimination (USD) is gradually expanding. The main innovative achievements of this paper are as follows: (1) Starting with the classical communication complexity of the multi-party appointment (MPD) problem, the quantum distributed algorithm of the MPD problem is studied, and the quantum communication complexity of the MPD problem is given. It is proved that the quantum communication complexity is at most close to the reduction of the quadratic polynomial level in comparison with the classical case. The results of the analysis verify the performance advantage of the quantum algorithm, especially when the number of users is large. (2) The classical communication complexity of the multi-party computing (MPC) problem based on the general discriminant function is studied, and the quantum distributed algorithm and the quantum communication complexity of the problem are given. The results show that the performance of the quantum algorithm is mainly dependent on the gap between the square root of the function definition domain and the number of users. The quantum communication complexity will be at most near the secondary polynomial level in comparison to the classical case. (3) To study the MPC problem based on the discriminant function and the number of the "solution" of the MPD problem, the corresponding "solution" number estimation algorithm is given. The results show that, for the MPC problem, the quantum phase estimation algorithm is used to estimate the number of the "solution", and the quantum communication complexity is equivalent to that of the quantum distributed algorithm; for the MPD problem, the number of the "solution" can be estimated by the performance of the approximate phase estimation algorithm without any multi-party communication. The effectiveness of the simulation is verified. (4) researching the USD measurement of the OOK modulated coherent state signal, and giving the analytic expression of the deterministic probability and the error probability in the background of the thermal noise field. Using the symmetry of the coherent state, the measurement of the coherent state signal under the BPSK modulation and QPSK modulation is further studied, and the analytical expressions of the deterministic probability and the error probability in the background of the thermal noise field are given. The results show that the existence of the thermal noise field makes the optimal USD measurement degenerate into a general quantum measurement, so it is impossible to measure the ideal USD in practice, and the average photon number of the thermal noise field determines the extent to which the USD measurement deviates from the ideal condition. (5) The multi-access channel model based on the symmetric coherent state is studied, and the analytical expression of the average inter-user interference is given. On the base of this model, a multi-user detection method based on USD measurement is studied, and an analytical expression for detecting error probability among users is given. The results show that, compared with the case of using MED to measure the error, the ideal USD measurement can be used to distinguish different users from the error area. (6) The two-site access channel model based on the symmetric coherent state is studied. On the basis of this model, an analytical expression of the error probability and the maximum channel capacity among the users based on the MED measurement and the USD measurement are respectively given. The research shows that the use of the USD measurement can be used for different users in the error area, but the maximum channel capacity is smaller than that of the MED measurement. In addition, the probability of error between users and the analytical expression of the maximum channel capacity are also given in the background of thermal noise field. The research shows that, with the increase of the average photon number of the thermal noise field from 0, the probability of user detection error measured with USD will gradually increase from the error of zero error, and the maximum channel capacity will gradually decrease from the noise-free condition. The results of the research on MPD and MPC show that the multi-party communication overhead can be effectively reduced by using the quantum distributed algorithm. The research on the measurement of the noise-free coherent states enriches the content of the coherent state signal quantum detection, and the efficiency of the quantum multi-user detection using the USD measurement is better than that of the MED method. These results are of theoretical and practical reference value to the further study of the optical quantum communication technology.
【学位授予单位】：南京邮电大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：O413;TN918

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