Extreme points of the set of quantum states with bounded energy
Stephan Weis, Максим Евгеньевич Широков · Russian Mathematical Surveys · 2021
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.