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arXiv · 0902.2634

Random repeated quantum interactions and random invariant states

Ion Nechita·Clément Pellegrini
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Abstract

We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between $\mathcal{H}$ and $\mathcal{K}_n$. The other involves random quantum states describing each copy $\mathcal{K}_n$. In the limit of a large number of interactions, we present convergence results for the asymptotic state of $\mathcal{H}$. 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 \emph{asymptotic induced ensemble}.

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Ion Nechita, Clément Pellegrini. 2009-02-16. Random repeated quantum interactions and random invariant states. https://doi.org/10.1007/s00440-010-0323-6

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