Random repeated quantum interactions and random invariant states

• 成果类型: Article
• 署名作者: Nechita, Ion; Pellegrini, Clement
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Kwazulu Natal; University of Kwazulu Natal
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0323-6
• 发表日期: 2012
• 页码: 299-320
• 关键词: Asymptotics; MAPS

摘要

We consider a generalized model of repeated quantum interactions, where a system H is interacting in a random way with a sequence of independent quantum systems K-n, n >= 1. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between H and Kn. The other involves random quantum states describing each copy K-n. In the limit of a large number of interactions, we present convergence results for the asymptotic state of H. This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the asymptotic induced ensemble.