Extreme points of the set of quantum states with bounded energy

• URL: http://arxiv.org/abs/2002.03969v1
• Date: Mon, 10 Feb 2020 17:30:43 GMT
• Title: Extreme points of the set of quantum states with bounded energy
• Abstract summary: We show that for any energy observable every extreme point of the set of quantum states with bounded energy is a pure state. We prove that any quantum state with finite energy can be represented as a continuous convex combination of pure states with the same energy.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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