A multi-ion optical clock with $\mathbf{5 \times 10^{-19}}$ uncertainty

Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below $1\times10^{-18}$. Scaling these systems to multiple, simultaneously interrogated ions reduces measurement times, driving recent advances in multi-ion clocks. However, maintaining state-of-the-art systematic uncertainties while increasing the number of ions remains a central challenge. Here, we report on a multi-ion optical atomic clock with a fractional frequency uncertainty of $5.3\times10^{-19}$ and up to 10 \Sr ions. Ion-resolved state detection enables minimization of position-dependent shifts, with residual effects suppressed below the $10^{-20}$-level. Clock operation with eight to ten ions reduces the measurement time by a factor of 4.8 compared to single-ion operation. A comparison with an established \Yb single-ion clock yields an unperturbed frequency ratio of $0.6926711632159660405(20)$, with a statistical uncertainty of $0.9\times10^{-18}$ and a combined uncertainty of $2.9\times 10^{-18}$. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.