Fig. 4: Coherence time and crosstalk.

a Protocol to measure the coherence time of communication qubit and memory qubit. We prepare the memory qubit in \(\vert {+}_{M}\rangle=\frac{\vert {\downarrow }_{M}\rangle+\vert {\uparrow }_{M}\rangle }{\sqrt{2}}\) (Fig. 2b), and apply a Ramsey measurement with a spin echo in the middle. We measure the memory qubit coherence time in both the case with ion-photon entangling (IPE) performed on the communication qubit (yellow shaded sequence) and the case without IPE (green shaded sequence). For the communication qubit, we prepare the communication qubit in \(\vert {+}_{C}\rangle=\frac{\vert {\downarrow }_{C}\rangle+\vert {\uparrow }_{C}\rangle }{\sqrt{2}}\) and apply a Ramsey measurement without spin echo (blue shaded sequence). b Measurement results. For the communication qubit, a fitting of Gaussian decay yields a coherence time of 5.8 ± 0.1 ms (blue triangle). The yellow square and the fitted curve show the fidelity decay in the memory qubit with all the noisy operations on the communication qubits applied. The extracted coherence time is 366 ± 11 ms. The green circle is the memory qubit fidelity in the case of no operations on the communication qubits, and the fitted coherence time is 368 ± 9 ms. The coherence time of memory qubit with or without operations on communication qubits cannot be faithfully distinguished considering the statistical error. The red diamonds characterize the spontaneous decay of the memory qubit after different storage times. The fitted lifetime of \(\vert {D}_{5/2}\rangle\) is 958 ms. The small discrepancy between our measurement result and the theoretical value ( ~1 s) can be attributed to the leaked 854 nm laser. All the coherence time is fitted by a Gaussian decay \(F=a\,{e}^{-{(x/\tau )}^{2}}+1/2\). Error bars represent one standard deviation in this figure.