Table 1 Key properties characterizing the QD hole spin and the waveguide device.

Emission wavelength

945 nm

External magnetic field B_y

2 T

The total decay rate of the QD Γ

(2.48 ± 0.02) ns⁻¹¹⁴

Ground-state Zeeman splitting Δ_h

2π × 7.3 GHz¹⁴

Optical cyclicity C = γ_Y/γ_X

14.7 ± 0.2⁴⁷

Waveguide-coupling efficiency β

(0.865 ± 0.059)

Standard deviation in spectral diffusion fluctuation σ_e

2π × (332 ± 15) MHz

Standard deviation in pulse spectral width σ_o

0.589 ns⁻¹

Pure dephasing rate γ_d

(0.099 ± 0.004) ns⁻¹

Spin-echo visibility V_s

(57.5 ± 0.4)%

Spin π-rotation fidelity F_π

(88.1 ± 3.8)%

Spin dephasing time \({T}_{2}^{* }\)

(23.2 ± 1.4) ns¹⁴

Spin coherence time \({T}_{2}^{{{{\rm{echo}}}}}\)

(448 ± 37) ns¹⁴

Duration of the entanglement measurement sequence τ_seq

606 ns