Extreme points of the set of quantum states with bounded energy

Abstract

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.

Preliminary version. Any comments and references are welcome

References in corpus (1)

• Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities

Cited by in corpus (3)

• Quantum Energy Lines and the optimal output ergotropy problem
• Optimal form of the Kretschmann-Schlingemann-Werner theorem for energy-constrained quantum channels and operations
• Energy-limited quantum dynamics