Generation of entanglement in a quantum wire and application to single-electron transmittivity

We present a novel method to generate entanglement between two fixed impurities in a 1D metallic/semiconductor chain without them having to interact directly, and then show how this entanglement can actually be used to control the electron transmittivity along the wire. First, we study how two magnetic impurities embedded in a solid can be entangled by an injected electron scattering between them and by subsequent measurement of the electron's state. We obtain the entanglement between the impurities as a function of the interaction strength of the electron-impurity coupling, and find that our scheme allows us to entangle the impurities maximally with a significant probability. While much work has been done on entangling spins in mesoscopic solid state systems, this is the first proposal for entangling stationary spins, which can be well separated, using a reduced control method. We then reverse to problem to analyze the electron transmittivity along the wire in the presence of entanglement between the impurity spins. We find that, for suitable values of the electron momentum, different entangled states of the impurities can: either make the wire fully transparent for the electron (independently of its spin state); either strongly inhibits the electron transmission. These striking predicted effects could be experimentally observed. Moreover, they could be applied to interfacing quantum computer registers, as well as to detect entanglement between solid state qubits.