Skip to main content

Research Repository

Advanced Search

Sanov and central limit theorems for output statistics of quantum Markov chains

Horssen, Merlijn van; Guţă, Mădălin

Authors

Merlijn van Horssen



Abstract

In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.

Journal Article Type Article
Publication Date Feb 18, 2015
Journal Journal of Mathematical Physics
Print ISSN 0022-2488
Electronic ISSN 1089-7658
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 56
Issue 2
Article Number 022109
APA6 Citation Horssen, M. V., & Guţă, M. (2015). Sanov and central limit theorems for output statistics of quantum Markov chains. Journal of Mathematical Physics, 56(2), https://doi.org/10.1063/1.4907995
DOI https://doi.org/10.1063/1.4907995
Keywords Quantum measurement theory, Eigenvalues , Signal generators , Statistical analysis, Markov processes
Publisher URL https://doi.org/10.1063/1.4907995
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

Files

Sanov 1.4907995.pdf (2.1 Mb)
PDF

Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





You might also like



Downloadable Citations

;