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

Abstract

The ability to transfer quantum information from one location to another with high probability 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 transfer probability. In this work we show that the addition of an impurity near each end point, coupled to the uniform chain with strength $w$, is sufficient to ensure efficient and high-probability state transfer. An eigenstate localized in the vicinity of the impurity can be tuned into resonance with chain-extended states by adjusting $w(N)\ensuremath{\propto}{N}^{1/2}$; the resulting avoided crossing yields resonant eigenstates with large amplitudes on the chain end points and approximately equidistant eigenvalues. The state transfer time scales as $t\ensuremath{\propto}{N}^{3/2}$, and its transfer probability $P$ approaches unity in the thermodynamic limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$; the error scales as $1\ensuremath{-}P\ensuremath{\propto}{N}^{\ensuremath{-}1}$. Thus, with the addition of two impurities, asymptotically perfect efficient state transfer with a uniform chain is possible even in the absence of external control.