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.

References

When we restrict the dynamics of the system to Markov dynamics, in particular a quantum master equation, we might give another type of trade-off relation between the measurement accuracy and the measurement time, but we leave this question as a future work.

— Speed-Accuracy Trade-Off Relations in Quantum Measurements and Computations  (2405.15291 - Nakajima et al., 2024) in Section s_7 (Summary)

Does finite propagation time impose a model-independent lower bound on correlations and entanglement between the systems and mediator for a prescribed effective interaction? Similarly, can the decoherence produced by local operations be bounded in terms of the mediator travel time, effective interaction strength, and control rate? What are the microscopic models that minimize these effects?

— Quantum models of interaction Hamiltonian and their paradoxes  (2609.11618 - Gisin et al., 10 Sep 2026) in Section 6, “Outlook” (subsection “Unavoidable correlations and decoherence”)