Perfect State Transfer in PT-symmetric Non-Hermitian Networks

TL;DR

This paper explores PT-symmetric non-Hermitian quantum networks, demonstrating conditions for perfect state transfer and highlighting the relationship between pseudo-Hermitian Hamiltonians and their Hermitian counterparts.

Contribution

It introduces a PT-symmetric version of a quantum network model, analyzing its potential for perfect state transfer within the unbroken PT-symmetry phase.

Findings

Conditional perfect state transfer in the unbroken PT phase

Evolution operator equivalent to PT operator at specific periods

Highlights the complex relationship between pseudo-Hermitian and Hermitian Hamiltonians

Abstract

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.