量子光源是光量子信息技术的重要功能单元。基于光纤中自发四波混频的光通信波段量子光源具有和当代光通信技术兼容的特点，在发展实用化光量子信息应用中有重要价值。本论文结合国家973计划项目课题“面向全量子网络的量子光源”，从量子信息研究和应用中对量子光源的要求出发研究光纤基量子光源的优化设计和物理实现。取得的研究成果包括： 实验实现了高质量光通信波段光纤关联双光子源和可预报单光子源。理论上解决了给定鉴维表达式的值作为约束的条件下鉴熵问题中量子最小熵的求解问题，利用光纤基关联双光子源实验验证了理论结果。并将光纤基可预报单光子源应用于鉴维问题，实验验证了不同维度下经典/量子系统的鉴维表达式$R_4$的界。研究工作表明光纤双光子源可以作为科研仪器用于量子信息基础实验等科研应用中。 提出了一种基于光纤Sagnac环中自发矢量四波混频和量子干涉的频率简并偏振纠缠双光子态产生方案，实验论证了该方案产生的偏振纠缠贝尔态可被贝尔态测量装置分辨，可用于偏振纠缠编码。进一步将该量子光源方案应用于光纤信道的量子安全直接通信研究，在经过500米色散位移光纤传输和2200米色散位移光纤构成的量子缓存器后，实验得到较好的偏振纠缠贝尔基检测结果。以此为基础对量子安全直接通信协议的光纤实现进行了性能估计，表明其具有在局域网和城域网中应用的潜力。 提出并实验论证了在时间片纠缠光子对的Franson型干涉实验中引入时域滤波器减小非平衡马赫曾德尔干涉仪臂长差的方案。实现了光通信波段光纤基时间片纠缠量子光源。采用400ps臂长差的非平衡马赫曾德尔干涉仪，通过测量两非正交相位基下的双光子干涉条纹可见度论证了方案的可行性。 系统研究了与量子力学互文性有关的若干理论问题。在对易关系和测量事项确定的情景下,理论上证明了非弦对易图是建立量子关联的充分必要条件而非完美排斥图则是建立量子关联的必要不充分条件；研究了在两个熵非互文性不等式之间的单婚性关系，证明了熵互文性不等式的单婚性关系可由将其正交图分解为完美子图的方法来建立，证明了正交图为共有两个交点的两个奇环时对应的两个熵不等式具有单婚性但两个KCBS 型不等式不具有单婚性；利用相干光源与功率计等经典光学实验器件，实验模拟了量子系统中非互文性Wright不等式的违背。
Generations of various photonic quantum states are basic and important functions in photonic quantum information technologies. The quantum light sources which are based on the spontaneous four wave mixing in optical fibers are compatible with technologies of optical fiber communications, showing great potential on practical quantum information applications. This dissertation focuses on the design and realization of telecom band fiber based quantum light sources, and extends their applications in quantum communication and quantum information. The main achievements include: High quality telecom band fiber based correlated biphoton source and heralded single photon source are realized experimentally. The correlated biphoton source is applied on the experimental test of quantum minimal entropy. While, the minimal quantum entropy under three widely used dimension witnesses are solved theoretically. On the other hand, the heralded single photon source is applied on the experimental verification of the upper bounds of dimension witness R4 for classical and quantum systems. These works show that fiber based quantum light sources can be used as important tools in experimental investigations on basic theories of quantum information. A generation scheme of frequency-degenerate polarization-entangled photon pairs based on spontaneous four wave mixing in processes in a fiber Sagnac loop is proposed and demonstrated experimentally. It is shown that the generated polarization Bell state can be discriminated by the simplified Bell State Measurements. Based on the frequency-degenerated polarization entangled photon pairs source, a quantum secure direct communication experiment is realized. In the experiment, two pieces of dispersion-shifted-fibers of 500meters long are used as the quantum channels, and two pieces of dispersion-shifted-fibers of 2200 meters long are used as quantum memories. The information is encoded on the polarization entangled Bell states of the photon pairs and decoded by the setup of Bell State Measurements. The performance of this fiber based quantum secure direct communication system is analyzed theoretically, showing its potential on applications in local and metropolitan area networks. A scheme of time domain filter is introduced into the Franson-type interference experiment for the telecom band time bin entangled photon pairs. The scheme reduce the requirement of the large arm differences in the unbalanced Mach-Zender interferometers used in Franson-type interference, which is mainly decided by the large time jitters of the single photon detectors in the near infrared band. Realizing the time domain filter by an electronic optical modulator, the scheme is demonstrated by the Franson type interference experiment utilizing unbalanced Mach-Zender interferometers with arm differences of 400 ps. Several theoretical works on the contextuality of quantum mechanics are carried out. It is proven that the non-chordal compatible graph is the necessary and sufficient condition for exhibiting quantum correlation while the imperfect exclusivity graph is the necessary but not sufficient condition for exhibiting quantum correlation in the compatible-fixed(event-fixed) scenario; It is proven that the monogamy relation between two entropic non-contextuality inequalities can be exhibited by decomposing the orthogonality graph into perfect subgraphs, showing that when orthogonality graph is made of two odd cycles with two common vertex, monogamy relation exists between two entropic non-contextuality inequalities while it does not exist between two KCBS-type inequalities. The violation of the Wright inequality is simulated by classical optics.
