Locality and error correction in quantum dynamics with measurement

Understand

The speed of light $c$ sets a strict upper bound on the speed of information transfer in both classical and quantum systems.

• In nonrelativistic quantum systems, the Lieb-Robinson Theorem imposes an emergent speed limit $v \hspace{-0.2mm} \ll \hspace{-0.2mm} c$, establishing locality under unitary evolution and constraining the time needed to perform useful quantum tasks.
• We extend the Lieb-Robinson Theorem to quantum dynamics with measurements.
• In contrast to the expectation that measurements can arbitrarily violate spatial locality, we find at most an $(M \hspace{-0.5mm} +\hspace{-0.5mm} 1)$-fold enhancement to the speed $v$ of quantum information, provided the outcomes of measurements in $M$ local regions are known.