
Explicit definition of PT symmetry for nonunitary quantum walks with gain and lossExplicit definition of PT symmetry for nonunitary quantum walks with gain and loss 
"/Mochizuki, Ken/"Mochizuki, Ken ,
"/Kim, Dakyeong/"Kim, Dakyeong ,
"/Obuse, Hideaki(1000050415121)/"Obuse, Hideaki
93
(
6
)
, p.062116 , 20160618 , American Physical Society (APS)
ISSN:24699926
Description
PT symmetry, that is, a combined parity and timereversal symmetry, is a key milestone for nonHermitian systems exhibiting entirely real eigenenergy. In the present work, motivated by a recent experiment, we study PT symmetry of the timeevolution 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 timeevolution 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 timeevolution operator. Applying these results, we clarify that the nonunitary quantum walk in the experiment does have PT symmetry.
FullText
http://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/62592/1/PhysRevA.93.062116.pdf