Hydrogen reionisation ends by $z=5.3$: Lyman-$\alpha$ optical depth measured by the XQR-30 sample

The presence of excess scatter in the Ly-$\alpha$ forest at $z\sim 5.5$, together with the existence of sporadic extended opaque Gunn-Peterson troughs, has started to provide robust evidence for a late end of hydrogen reionisation. However, low data quality and systematic uncertainties complicate the use of Ly-$\alpha$ transmission as a precision probe of reionisation's end stages. In this paper, we assemble a sample of 67 quasar sightlines at $z>5.5$ with high signal-to-noise ratios of $>10$ per $\leq 15$ km s$^{-1}$ spectral pixel, relying largely on the new XQR-30 quasar sample. XQR-30 is a large program on VLT/X-Shooter which obtained deep (SNR $>20$ per pixel) spectra of 30 quasars at $z>5.7$. We carefully account for systematics in continuum reconstruction, instrumentation, and contamination by damped Ly-$\alpha$ systems. We present improved measurements of the mean Ly-$\alpha$ transmission over $4.9 3.5 \sigma$). Our results indicate that reionisation-related fluctuations, whether in the UVB, residual neutral hydrogen fraction, and/or IGM temperature, persist in the intergalactic medium until $z=5.3$ ($t=1.1$ Gyr after the Big Bang). This is further evidence for a late end to reionisation.