Fig. 3: Improvements required to connect the Dutch cities of Delft and Eindhoven using color-center (CC) and trapped-ion (TI) repeaters for an entanglement-generation rate of 0.1 Hz and an average teleportation fidelity of 0.8717 (Target 1) and a rate of 0.5 Hz and average teleportation fidelity of 0.8571 (Target 2).

a The values that are required for the photon detection probability excluding attenuation losses and the coherence time. The baseline parameter values have been demonstrated in state-of-the-art experiments. The absolute minimal requirements are the required parameter values assuming that there are no other sources of noise or loss with the exception of fiber attenuation. The coherence-time values in the table are the communication-qubit dephasing time for CC and the collective dephasing time for TI (see Section “Methods” for an explanation of these parameters). The TI requirements are for running a double-click entanglement-generation protocol. The CC requirements are for running a double-click protocol for Target 1, and a single-click protocol for Target 2. We note that all the minimal requirements found have a photon detection probability excluding attenuation losses above 30%, the current state-of-the-art value for frequency conversion⁷⁵. b, c Directions along which hardware must be improved to connect the Dutch cities of Delft and Eindhoven using, respectively, a CC or a TI repeater. The further away the line is from the center towards a given parameter, the larger improvement that parameter requires. Improvement is measured in terms of the “improvement factor'', which tends to infinity as a parameter tends to its perfect value (see Section “Methods” for the definition). In both plots, a logarithmic scale is used. The origin of the plots corresponds to an improvement factor of 1, i.e., no improvement with respect to the state of the art. b (CC), the blue (orange) line corresponds to the minimal requirements for Target 1 (Target 2). Improvement is depicted for the following parameters, clockwise from the top: photon detection probability excluding attenuation losses in fiber, dephasing time of the communication qubit, dephasing time of the memory qubit, noise in the two-qubit gate, visibility of photon interference and dephasing noise induced on memory qubits when entanglement generation is attempted. c (TI), the line corresponds to the minimal requirements for Target 1. Improvement is depicted for the following parameters, clockwise from the top: photon detection probability excluding attenuation losses in fiber, qubit collective dephasing coherence time, spin-photon emission fidelity, visibility of photon interference and probability that two emitted photons coincide at the detection station. All parameters are explained in section “Methods”, and their state-of-the-art values that are being improved upon are given in Table 1.