关于量子超光速通信的一个理论设想

本文深入分析了拟议中的量子超光速通信理论,提出了实现量子超光速通信的原理与技术方案。此外,本文还讨论了适用于量子超光速通信的新的时空变换,并提出了两种检测特惠Lorentz参照系的实验方法。     

两粒子非最大纠缠态的量子非局域性

利用Bell—CHSH(Clauser—Horne—Shimony—Holt)不等式研究两个自旋为1／2的原子所构成的量子态的量子非局域性，计算表明两个自旋为1／2的原子所构成的非最大纠缠态，它的量子非局域性与量子态之间的纠缠度和极角有关；而所构成的最大纠缠态的非局域性只与极角有关。     

Bell型空间非定域性研究现状与展望

尽管和经典理论一样,从非相对论量子力学到相对论量子场论的量子理论采用了定域描述的方法,但本质上,量子理论却是在定域描述外衣下的空间非定域理论.从著名的EPR佯谬发难,Bell不等式的提出,GHZ定理,Hardy定理到Cabello定理,长期以来围绕Bell-GHZ-Hardy-Cabello这条空间非定域性研究路线,涌现出大量的理论和实验工作,文献汗牛充栋.迄今实验结果总是支持量子理论,但远远没能揭示出量子理论空间非定域性的本质,也未能否定隐变量的存在.这种状况使这一热点问题仍然吸引着很多人的关注和思考.我们对这条研究路线作了全面而简要地总结,系统而明确地叙述了有关的思想、概念和定理,最后给出了对它的详细评论.     

量子力学和相对论的结合、不相容及发展

基于量子力学和相对论的比较,二者既可以结合又存在不相容.由此讨论它们的某些可能的发展方向.特别探讨了3个方面:测不准原理和光速恒定等的矛盾;量子的非局域性显示出纠缠态应该是一种新的作用距离和强度中等的相互作用;由Dirac负能态推导出的负物质可能是一种暗物质.       

Foundations of quantum gravity: The role of principles grounded in empirical reality

When attempting to assess the strengths and weaknesses of various principles in their potential role of guiding the formulation of a theory of quantum gravity, it is crucial to distinguish between principles which are strongly supported by empirical data – either directly or indirectly – and principles which instead (merely) rely heavily on theoretical arguments for their justification. Principles in the latter category are not necessarily invalid, but their a priori foundational significance should be regarded with due caution. These remarks are illustrated in terms of the current standard models of cosmology and particle physics, as well as their respective underlying theories, i.e., essentially general relativity and quantum (field) theory. For instance, it is clear that both standard models are severely constrained by symmetry principles: an effective homogeneity and isotropy of the known universe on the largest scales in the case of cosmology and an underlying exact gauge symmetry of nuclear and electromagnetic interactions in the case of particle physics. However, in sharp contrast to the cosmological situation, where the relevant symmetry structure is more or less established directly on observational grounds, all known, nontrivial arguments for the “gauge principle” are purely theoretical (and far less conclusive than usually advocated). Similar remarks apply to the larger theoretical structures represented by general relativity and quantum (field) theory, where – actual or potential – empirical principles, such as the (Einstein) equivalence principle or EPR-type nonlocality, should be clearly differentiated from theoretical ones, such as general covariance or renormalizability. It is argued that if history is to be of any guidance, the best chance to obtain the key structural features of a putative quantum gravity theory is by deducing them, in some form, from the appropriate empirical principles (analogous to the manner in which, say, the idea that gravitation is a curved spacetime phenomenon is arguably implied by the equivalence principle). Theoretical principles may still be useful however in formulating a concrete theory (analogous to the manner in which, say, a suitable form of general covariance can still act as a sieve for separating theories of gravity from one another). It is subsequently argued that the appropriate empirical principles for deducing the key structural features of quantum gravity should at least include (i) quantum nonlocality, (ii) irreducible indeterminacy (or, essentially equivalently, given (i), relativistic causality), (iii) the thermodynamic arrow of time, (iv) homogeneity and isotropy of the observable universe on the largest scales. In each case, it is explained – when appropriate – how the principle in question could be implemented mathematically in a theory of quantum gravity, why it is considered to be of fundamental significance and also why contemporary accounts of it are insufficient. For instance, the high degree of uniformity observed in the Cosmic Microwave Background is usually regarded as theoretically problematic because of the existence of particle horizons, whereas the currently popular attempts to resolve this situation in terms of inflationary models are, for a number of reasons, less than satisfactory. However, rather than trying to account for the required empirical features dynamically, an arguably much more fruitful approach consists in attempting to account for these features directly, in the form of a lawlike initial condition within a theory of quantum gravity.     

半线性方程的非局部问题

考虑源于拟静态热弹性的一类半线性抛物型偏微分方程的非线性非局部边值问题，证明了局部解的存在性，比较定理，讨论了解的大时间性态；在较弱的条件下得到了极大、极小解的存在性，并给出了不适定的两个例子．     

广义GHZ态的制备和非定域性的测量

我们用参量下转换的方法,合理设计实验方案,制备了广义GHZ（Greenberger-Horne-Zeilinger）三体偏振纠缠态,测量了所制备状态的密度矩阵,并通过密度矩阵计算出了状态相对于目标态的保真度.实验制备出了保真度达0.85左右的高保真三体纠缠态.测量了GGHZ（generalized GHZ）纠缠态的Bell-Mermin算符期望值,得到了和理论计算一致的测量结果.结果表明,量子态非定域特性与体系的纠缠程度密切相关,这说明制备GGHZ纠缠态的方案和非定域特性的测量方法是可行的.     

高纯四光子GHZ态的实验制备及非定域性研究

采用Ⅱ型参量下转换（SPDC）和后选择技术,实验上制备了保真度达0．831的高纯四光子Greenberger—Home—Zeilinger（GHZ）态．通过理论分析和实验优化,提出一种有效提高四光子对比度的实验方法．同时利用制备的纠缠态,研究了四光子GHZ态的非定域性,得到了对四光子Bell不等式28标准差的偏离,证明制备的态为真正四体纠缠态．本文的研究对实验上获得高对比度的多光子纠缠态及非定域性研究具有非常好的借鉴意义．     

量子非局域性的应用与度量

随着量子计算机研究的进一步深入，量子态非局域性的理论日益重要，尤其是如何度量非局域性的大小．本文解释度量非局域性的大小的原则及介绍了一些主要的应用方向．     

双模减单光子压缩真空态的量子退相干和非局域性动力学

本文研究了双模减单光子压缩真空态的量子退相干和非局域性动力学．数值计算了相对熵纠缠度和计算分析了线性熵纠缠度．并进一步计算了基于膺自旋算符的Bell不等式，发现Bell不等式总是违背的．因此，可以确定退相干只能减少双模减单光子压缩真空态的纠缠量，不能完全消除纠缠．