Asymptotically perfect efficient quantum state transfer across uniform chains with two impurities
Xining Chen, Robert Mereau, David L. Feder · Physical Review A · 2016
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.