Quantum states as countable convex combination of pure states with bounded energy

• URL: http://arxiv.org/abs/2407.05950v1
• Date: Tue, 2 Jul 2024 20:53:53 GMT
• Title: Quantum states as countable convex combination of pure states with bounded energy
• Abstract summary: In infinite dimension states, given a state with energy bounded by E, we can write the state as a countable convex combination of pure states with energy bounded by E. We conclude that for a Hamiltonian satisfying the Gibb's hypothesis such states cannot exist.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We give response to the question: in infinite dimension states,given a state with energy bounded by E, we can write the state as a countable convex combination of pure states with energy bounded by E. We review the Alicki-Fannes-Winter technique to obtain a uniform continuity bound for the von Neumann entropy in states that are a mix of pure states with bounded energy, using this bound we conclude that for a Hamiltonian satisfying the Gibb's hypothesis such states cannot exist.

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