论文标题
广义量子模型中的非对称过渡概率
Non-symmetric transition probability in generalized qubit models
论文作者
论文摘要
量子机械过渡概率是对称的。在前面的两篇论文中引入了概率动机和更一般的量子逻辑定义，而没有假定其对称性，但是在所有示例中，它仍然对其进行对称。在这里，我们提出了一类二进制模型，其中使用单位空间中的单位间隔的极端点作为量子逻辑。我们表明，它们的状态空间严格凸出光滑的紧凑型凸组集，并且每个这样的集合都会带有状态空间K的量子逻辑。过渡概率是对称的，如果F k是希尔伯特空间中的单位球。在这种情况下，量子逻辑与自旋因子的投影晶格相同，这是一种特殊的正式Jordan代数。
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but in all the examples considered there it remains symmetric. Here we present a class of binary models where the transition probability is not symmetric, using the extreme points of the unit interval in an order unit space as quantum logic. We show that their state spaces are strictly convex smooth compact convex sets and that each such set K gives rise to a quantum logic of this class with the state space K. The transition probabilities are symmetric iff K is the unit ball in a Hilbert space. In this case, the quantum logic becomes identical with the projection lattice in a spin factor which is a special type of formally real Jordan algebra.
