Abstract
A quantum walk, that is, a synthetic quantum system mainly impremented by photonic systems, whose dynamics is described by a time-evolution operator, provides potential applications for quantum computing and information. It is further interesting that the quantum walk possesses novel topological phases akin to those of Floquet topological insulators, which are topological insulators driven by a time-periodic field[1,2]. Recently, a one-dimensional quantum walk dynamics associated with gain and loss is experimentally implemented by optical fiber loops [3]. The experiment shows that the energy of the system is kept to be real as a manifestation of PT symmetry (combined parity and time-reversal symmetry) in spite of the open quantum system.
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