Dynamical decoupling of unbounded Hamiltonians

Christian Arenz, Daniel Burgarth, Paolo Facchi, Robin Hillier

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

Original languageEnglish
Article number032203
Pages (from-to)1-16
Number of pages16
JournalJournal of Mathematical Physics
Issue number3
Publication statusPublished - Mar 2018
Externally publishedYes


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