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arXiv · 1603.05820

Explicit definition of $\mathcal{PT}$ symmetry for non-unitary quantum walks with gain and loss

Ken Mochizuki·Dakyeong Kim·Hideaki Obuse
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Abstract

$\mathcal{PT}$ 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 $\mathcal{PT}$ symmetry of the time-evolution operator of non-unitary quantum walks. We present the explicit definition of $\mathcal{PT}$ symmetry by employing a concept of symmetry time frames. We provide a necessary and sufficient condition so that the time-evolution operator of the non-unitary quantum walk retains $\mathcal{PT}$ 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 non-unitary quantum walk in the experiment does have $\mathcal{PT}$ symmetry.

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Ken Mochizuki, Dakyeong Kim, Hideaki Obuse. 2016-03-18. Explicit definition of $\mathcal{PT}$ symmetry for non-unitary quantum walks with gain and loss. https://doi.org/10.1103/physreva.93.062116

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