Ancilla mediated qubit readout and heralded entanglement between rare-earth dopant ions in crystals

Abstract: Owing to their long excited state lifetimes, rare-earth ions in crystals are widely used in quantum applications. To allow optical readout of the qubit state of individual ions, we propose to dope the crystal with an additional nearby ancilla ion with a shorter radiative lifetime. We show how a Bayesian analysis exhausts the information about the state of the qubit from the optical signal of the ancilla ion. We study the effects of incoherent processes and propose ways to reduce their effect on the readout. Finally, we extend the architecture to ions residing in two remote cavities, and we show how continuous monitoring of fluorescence signals from the two ancilla ions leads to entanglement of the qubit ions.