On the distribution of the mean energy in the unitary orbit of quantum states

Abstract

Given a closed quantum system, the states that can be reached with a cyclic process are those with the same spectrum as the initial state. Here we prove that, under a very general assumption on the Hamiltonian, the distribution of the mean extractable work is very close to a gaussian with respect to the Haar measure. We derive bounds for both the moments of the distribution of the mean energy of the state and for its characteristic function, showing that the discrepancy with the normal distribution is increasingly suppressed for large dimensions of the system Hilbert space.

34 pages, 1 figure Expanded the introduction; minor editing

References in corpus (7)

• Quantum information with Gaussian states
• Evenly distributed unitaries: on the structure of unitary designs
• Optimizing quantum process tomography with unitary 2-designs
• Distribution of work in isothermal non-equilibrium processes
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Work distribution for the driven harmonic oscillator with time-dependent strength: Exact solution and slow driving
• Revisiting SU(N) integrals

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• Efficiency fluctuations in a quantum battery charged by a repeated interaction process