Explicit definition of $\mathcal{PT}$ symmetry for non-unitary quantum walks with gain and loss
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| Format: | Preprint |
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2016
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| _version_ | 1866913641617424384 |
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| author | Mochizuki, Ken Kim, Dakyeong Obuse, Hideaki |
| author_facet | Mochizuki, Ken Kim, Dakyeong Obuse, Hideaki |
| contents | $\mathcal{PT}$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1603_05820 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Explicit definition of $\mathcal{PT}$ symmetry for non-unitary quantum walks with gain and loss Mochizuki, Ken Kim, Dakyeong Obuse, Hideaki Quantum Physics Mesoscale and Nanoscale Physics Optics $\mathcal{PT}$ 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. |
| title | Explicit definition of $\mathcal{PT}$ symmetry for non-unitary quantum walks with gain and loss |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Optics |
| url | https://arxiv.org/abs/1603.05820 |