Speed–accuracy trade-off under Markovian (quantum master equation) dynamics

Develop a trade-off relation between measurement time and measurement accuracy for quantum measurements when the total dynamics is restricted to Markovian dynamics, specifically dynamics governed by a quantum master equation, in contrast to the non-Markovian generality treated here. Precisely, derive an explicit, operationally meaningful inequality relating measurement duration and a well-defined measurement error (e.g., irreversibility-based error or its established lower bounds) under a Markovian quantum master equation model for the system–apparatus evolution.

Background

The paper establishes universal speed–accuracy trade-off relations for quantum measurements and computations based on energy conservation and locality, using Lieb–Robinson bounds, without assuming Markovian dynamics. These results apply even to complex, non-Markovian evolutions.

The authors note that if one restricts to Markovian dynamics, particularly quantum master equations, a different (potentially tighter or structurally distinct) trade-off relation may be obtainable. Identifying and proving such a Markovian-specific speed–accuracy trade-off is left open.