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 asymptotic induced ensemble.
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Nechita, I., Pellegrini, C. Random repeated quantum interactions and random invariant states. Probab. Theory Relat. Fields 152, 299–320 (2012). https://doi.org/10.1007/s00440-010-0323-6
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DOI: https://doi.org/10.1007/s00440-010-0323-6
Keywords
- Quantum repeated interactions
- Random quantum channels
- Random matrices
- Peripheral spectrum
- Random density matrices
Mathematics Subject Classification (2000)
- Primary 15A52
- Secondary 94A40
- 60F15