Explicit definition of symmetry for non-unitary quantum walks with gain and loss
arXiv:1603.05820 · doi:10.1103/PhysRevA.93.062116
Abstract
symmetry, that is, a combined parity and time-reversal symmetry is a key milestone for non-Hermite systems exhibiting entirely real eigenenergy. In the present work, motivated by a recent experiment, we study symmetry of the time-evolution operator of non-unitary quantum walks. We present the explicit definition of symmetry by employing a concept of symmetry time frames. We provide a necessary and sufficient condition so that the time-evolution operator of the non-unitary quantum walk retains 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 non-unitary quantum walk in the experiment does have symmetry.
14 pages, 8 figures
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