On the distribution of the mean energy in the unitary orbit of quantum states
Raffaele Salvia, Vittorio Giovannetti
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.
Topics & Concepts
Distribution (mathematics)Unitary stateMathematicsState (computer science)GaussianQuantum statePhysicsQuantum mechanicsQuantumWork (physics)Spectrum (functional analysis)Orbit (dynamics)Energy (signal processing)Energy spectrumHilbert spaceStatistical physicsMathematical analysisQuantum systemProbability distributionCoherent statesHaar measureEnergy distributionDistribution functionUnitary groupGroup (periodic table)Mathematical physicsSpectral Theory in Mathematical PhysicsQuantum chaos and dynamical systemsMathematical Approximation and Integration