论文标题
局部断层扫描和复数在量子力学中的作用
Local tomography and the role of the complex numbers in quantum mechanics
论文作者
论文摘要
有限维量子力学的各种重建导致正式的Jordan代数A和最后一步得出结论，即A是C*-Algebra的自动参与部分。使用量子逻辑设置，可以表明可以通过假设有一个由同一系统的两个副本组成的复合系统的局部层析成像模型来实现。局部断层扫描是经典概率理论和量子力学的特征。这意味着可以通过所有子系统中的同时测量来执行多部分系统的状态断层扫描。局部断层扫描的量子逻辑定义足够，但是与文献中普遍的定义相比，它的余额较小，并且涉及一些有关所谓的自旋因子的微妙之处。
Various reconstructions of finite-dimensional quantum mechanics result in a formally real Jordan algebra A and a last step remains to conclude that A is the self-adjoint part of a C*-algebra. Using a quantum logical setting, it is shown that this can be achieved by postulating that there is a locally tomographic model for a composite system consisting of two copies of the same system. Local tomography is a feature of classical probability theory and quantum mechanics; it means that state tomography for a multipartite system can be performed by simultaneous measurements in all subsystems. The quantum logical definition of local tomography is sufficient, but it is less restictive than the prevalent definition in the literature and involves some subtleties concerning the so-called spin factors.
