Perfect State Transfer in PT-symmetric Non-Hermitian Networks

We systematically study the parity- and time-reversal (PT) symmetric non-Hermitian version of a quantum network proposed in the paper of Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)]. The nature of this model shows that it is a paradigm to demonstrate the complex relationship between the pseudo-Hermitian Hamiltonian and its Hermitian counterpart as well as a candidate in the experimental realization to simulate PT-symmetry breaking. We also show that this model allows a conditional perfect state transfer within the unbroken PT-symmetry region but not an arbitrary one. This is due to the fact that the evolution operator at a certain period is equivalent to the PT operator for the real-valued wave function in the elaborate PT-symmetric Hilbert space.