Explicit definition of PT symmetry for nonunitary quantum walks with gain and loss

Ken Mochizuki, Dakyeong Kim, Hideaki Obuse

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)


PT symmetry, that is, a combined parity and time-reversal symmetry, is a key milestone for non-Hermitian systems exhibiting entirely real eigenenergy. In the present work, motivated by a recent experiment, we study PT symmetry of the time-evolution operator of nonunitary quantum walks. We present the explicit definition of PT symmetry by employing a concept of symmetry time frames. We provide a necessary and sufficient condition so that the time-evolution operator of the nonunitary quantum walk retains PT symmetry even when parameters of the model depend on position. It is also shown that there exist extra symmetries embedded in the time-evolution operator. Applying these results, we clarify that the nonunitary quantum walk in the experiment does have PT symmetry.

Original languageEnglish
Article number062116
JournalPhysical Review A
Issue number6
Publication statusPublished - 2016 Jun 17
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


Dive into the research topics of 'Explicit definition of PT symmetry for nonunitary quantum walks with gain and loss'. Together they form a unique fingerprint.

Cite this