Asymptotically perfect efficient quantum state transfer across uniform chains with two impurities

The ability to transfer quantum information from one location to another with high fidelity is of central importance to quantum information science. Unfortunately for the simplest system of a uniform chain (a spin chain or a particle in a one-dimensional lattice), the state transfer time grows exponentially in the chain length $N$ at fixed fidelity. In this work we show that the addition of an impurity near each endpoint, coupled to the uniform chain with strength $w$, is sufficient to ensure efficient and high-fidelity state transfer. An eigenstate localized in the vicinity of the impurity can be tuned into resonance with chain extended states by tuning $w(N)\propto N^{1/2}$; the resulting avoided crossing yields resonant eigenstates with large amplitudes on the chain endpoints and approximately equidistant eigenvalues. The state transfer time scales as $t\propto N^{3/2}$ and its fidelity $F$ approaches unity in the thermodynamic limit $N\to\infty$; the error scales as $1-F\propto N^{-1}$. Thus, with the addition of two impurities, asymptotically perfect state transfer with a uniform chain is possible even in the absence of external control.