相対論的量子測定理論及び相対論的量子情報理論の研究

这个项目的目标是通过研究相对论如何影响纠缠系统，将量子信息理论扩展到相对论领域。我们主要研究洛伦兹增强如何改变不同几何形状的大质量两体自旋1/2系统的纠缠。由于这些系统不接受解析处理，我们借助于数值方法计算了具有不同乘积和纠缠态动量的两粒子系统的自旋自由度与由Bell态给出的自旋的重合度。动量采用高斯形式，几何形状确保自旋经历最大维格纳旋转。我们还得到了自旋态的对角表示，使我们能够以三维方式表示自旋轨道，从而进一步从几何上洞察自旋态的行为。这些结果意义重大，因为它们将纠缠理论扩展到相对论体制。纠缠意味着量子系统表现出从经典观点来看不可能实现的关联。在量子信息论中，纠缠被视为一种资源，它承诺采用新技术来实现超越经典理论的信息处理任务。从理论和实践的角度来看，实现纠缠的相对论解释都很重要，因为正确的现实理论是相对论的。这些结果有助于解释相对论中量子信息的行为；它们也有助于将量子信息的应用扩展到相对论系统。

This project has the goal of extending quantum information theory to the relativistic domain by studying how relativity affects entangled systems. We focus on how Lorentz boosts change the entanglement of massive bipartite spin-1/2 systems in various geometries. Since these systems do not admit analytic treatment, we resort to numerical methods to calculate the concurrence of spin degrees of freedom of a two particle system with momenta in various product and entangled states, with the spins given by the Bell state. The momenta took the form of Gaussians and the geometry ensured that the spins undergo maximal Wigner rotation. We also obtained the diagonal representation of the spin state, allowing us to represent the spin orbits in a three dimensional manner, thereby giving further geometric insight into the behavior of the state. These results are significant because they extend the theory of entanglement to the relativistic regime. Entanglement means that quantum systems exhibit correlations which are not possible from the classical point of view. In quantum information theory entanglement is viewed as resource that promises new technologies which enable information processing tasks that are beyond the classical theory. Achieving a relativistic account of entanglement is important both from the theoretical and practical vantage point since the correct theory of reality is relativistic. These results contribute to the goal of explaining the behavior of quantum information in relativity; they also help extend applications of quantum information to relativistic systems.