  Currently most progresses on quantum secret sharing suffer from rate-distance
bound, and thus the key rates are limited. In addition to the limited key rate,
the technical difficulty and the corresponding cost together prevent
large-scale deployment. Furthermore, the performance of most existing protocols
is analyzed in the asymptotic regime without considering participant attacks.
Here we report a measurement-device-independent quantum secret sharing protocol
with improved key rate and transmission distance. Based on spatial
multiplexing, our protocol shows it can break rate-distance bounds over network
under at least ten communication parties. Compared with other protocols, our
work improves the secret key rate by more than two orders of magnitude and has
a longer transmission distance. We analyze the security of our protocol in the
composable framework considering participant attacks and evaluate its
performance in the finite-size regime. In addition, we investigate applying our
protocol to digital signatures where the signature rate is improved more than
$10^7$ times compared with existing protocols. We anticipate that our quantum
secret sharing protocol will provide a solid future for multiparty applications
on the quantum network.
