【摘要】：在量子通信復(fù)雜度的相關(guān)研究中,任意多方計算模型的通信復(fù)雜度研究越來越受到人們的關(guān)注。在光場相干態(tài)信號的量子檢測方面,最小差錯區(qū)分(MED)測量的研究已有較好的結(jié)果,而相干態(tài)非含糊狀態(tài)區(qū)分(USD)的研究工作正在逐漸展開。本文就此進行分析和研究,其主要創(chuàng)新性成果如下:(1)從多方約會(MPD)問題的經(jīng)典通信復(fù)雜度入手,研究MPD問題的量子分布式算法,給出MPD問題的量子通信復(fù)雜度,證明了其量子通信復(fù)雜度與經(jīng)典情況相比最多有接近二次多項式級的降低。分析結(jié)果驗證了量子算法的性能優(yōu)勢,尤其當(dāng)用戶數(shù)很大時,這種優(yōu)勢將更加明顯。(2)研究基于通用判別函數(shù)的多方計算(MPC)問題的經(jīng)典通信復(fù)雜度,給出該問題的量子分布式算法和量子通信復(fù)雜度。研究結(jié)果表明,量子算法的性能主要取決于函數(shù)定義域的平方根與用戶數(shù)之間的無窮大階的差距。量子通信復(fù)雜度較之經(jīng)典情形最多將會有接近二次多項式級的降低。(3)研究基于判別函數(shù)的MPC問題和MPD問題的“解”數(shù)量估計,給出相應(yīng)的“解”數(shù)量估計算法。研究結(jié)果表明:對于MPC問題,使用量子相位估計算法估計“解”的數(shù)量,其量子通信復(fù)雜度與量子分布式算法相當(dāng);對于MPD問題,無需任何多方通信就能夠以近似相位估計算法的效能估算出“解”的數(shù)量。仿真實驗驗證了其有效性。(4)研究OOK調(diào)制相干態(tài)信號的USD測量,給出它在熱噪聲場背景下的確定性概率和差錯概率的解析表達式。利用相干態(tài)的對稱性,進一步研究了BPSK調(diào)制和QPSK調(diào)制下的相干態(tài)信號的USD測量,分別給出它們在熱噪聲場背景下確定性概率和差錯概率的解析表達式。研究結(jié)果表明,熱噪聲場的存在使得最優(yōu)USD測量退化成一般量子測量,因此在實際中實現(xiàn)理想USD測量是不可能的,且熱噪聲場的平均光子數(shù)大小決定了USD測量偏離理想狀況的程度。(5)研究基于對稱相干態(tài)的多址接入信道模型,給出其平均用戶間干擾的解析表達式。在此模型的基礎(chǔ)上,研究基于USD測量的多用戶檢測方法,給出用戶間檢測差錯概率的解析表達式。研究結(jié)果表明,較之采用MED測量出現(xiàn)差錯的情況,采用理想USD測量可以無差錯地區(qū)分不同用戶。(6)研究基于對稱相干態(tài)的二址接入信道模型。在此模型的基礎(chǔ)上,分別給出基于MED測量和USD測量的用戶間檢測差錯概率以及最大信道容量的解析表達式。研究表明,采用USD測量可以無差錯地區(qū)分不同用戶,但是最大信道容量卻比采用MED測量來得小。此外,還給出熱噪聲場背景下采用USD測量的用戶間檢測差錯概率以及最大信道容量的解析表達式。研究表明,隨著熱噪聲場平均光子數(shù)從0開始逐漸增高,采用USD測量的用戶檢測差錯概率將從無差錯開始逐步增大,最大信道容量將從無噪聲情況開始逐步減小。針對MPD和MPC等問題的研究結(jié)果表明,采用量子分布式算法能夠有效地降低多方通信開銷。含噪相干態(tài)USD測量的研究豐富了相干態(tài)信號量子檢測的內(nèi)容,并且采用USD測量的量子多用戶檢測的效能優(yōu)于MED方式。這些成果對光量子通信技術(shù)的進一步研究,具有理論意義和應(yīng)用參考價值。
[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.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：O413;TN918

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