Law of large numbers and central limit theorem for ergodic quantum processes

2023/03/15 by Lubashan Pathirana, Pathirana, Lubashan, Jeffrey Schenker +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2303.08992

openalex publication_date 2023/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 was recently obtained by Movassagh and Schenker. Under irreducibility and mixing conditions, we obtain a central limit type theorem describing fluctuations around the ergodic limit.

Citations

• Products of Random Matrices

Cited by

• Correlation Lengths for Stochastic Matrix Product States
• The Central Limit Theorem for random exponents on a Hilbert space in the Weak Operator Topology
• Asymptotic Behavior of Random Time-Inhomogeneous Markovian Quantum Dynamics
• The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces

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