Exact nonequilibrium quantum observable statistics: A large-deviation approach

Year: 2019

Authors: Gherardini S.

Autors Affiliation: Department of Physics and Astronomy & LENS, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy; Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy.

Abstract: The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the measurement outcomes at the end of the system?s evolution are random variables. Here, we provide the exact large-deviation form of their probability distribution, which is given by an exponentially decaying profile in the number of measurements. The most probable distribution of the measurement outcomes in a single realization of the system transformation is then derived, thus achieving predictions beyond the expectation value. The theoretical results are confirmed by numerical simulations of an experimentally reproducible two-level system with stochastic Hamiltonian.


Volume: 99 (6)      Pages from: 062105-1  to: 062105-9

More Information: The author gratefully acknowledges F. Caruso and M. Artoni for a detailed reading of the paper, A. Trombettoni and M. Fattori for several useful comments, and Shamik Gupta for insightful discussions on LD theory, in particular, on the derivation of the measurement outcomes´ probability distribution. S.G. was financially supported from the Fondazione Cassa di Risparmio di Firenze through the project Q-BIOSCAN.
KeyWords: Quantum statistical mechanics, Large deviation theory, Rare event statistics
DOI: 10.1103/PhysRevA.99.062105