能量有界的量子态集的极值点
Extreme points of the set of quantum states with bounded energy
摘要：
我们证明了对于任何可观测的能量，能量有界的量子态集合的每个极值点都是纯态。这使得我们可以用有界能量的纯态的连续凸组合来表示每一个有界能量的态。进一步，我们证明了任何有限能量的量子态都可以表示为具有相同能量的纯态的连续凸组合。我们讨论的例子从量子信息理论。
英文摘要：
We show that for any energy observable every extreme point of the set of quantum states with bounded energy is a pure state. This allows us to write every state with bounded energy in terms of a continuous convex combination of pure states of bounded energy. Furthermore, we prove that any quantum state with finite energy can be represented as a continuous convex combination of pure states with the same energy. We discuss examples from quantum information theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
