A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum operation with noise. Such ergodic quantum processes generalize independent quantum processes. An ergodic theorem describing convergence to equilibrium for a general class of such processes has been recently obtained by Movassagh and Schenker. Under irreducibility and mixing conditions, we obtain a central limit type theorem describing fluctuations around the ergodic limit.
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Research Article| August 30 2023
Law of large numbers and central limit theorem for ergodic quantum processes
Special Collection: New Directions in Disordered Systems: In Honor of Abel Klein
Lubashan Pathirana ;
Lubashan Pathirana, Jeffrey Schenker; Law of large numbers and central limit theorem for ergodic quantum processes. J. Math. Phys. 1 August 2023; 64 (8): 082201. https://doi.org/10.1063/5.0153483
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