Quantum States as Countable Convex Combination of Pure States with Bounded Energy

Juan Pablo Lopez

Juan Pablo Lopez

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.

Hans Luth

Stephan Weis, Максим Евгеньевич Широков

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.

Hans Luth

Lihua Yang, Jinchuan Hou

In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structure theorem for maps between multipartite quantum states that preserve separable pure states and strict convex combinations is established. Then, these results are applied to characterize injective (local) quantum measurements and answer some conjectures proposed in Hou and Liu (2012 J. Phys. A: Math. Theor. 45 205305).