Quantum speed limit under decoherence: unitary, dissipative, and fluctuation contributions

TL;DR

This paper derives a new quantum speed limit for open systems, decomposing the evolution into unitary, dissipative, and fluctuation parts, revealing fundamental trade-offs between speed, distinguishability, and information precision.

Contribution

It introduces an analytically computable bound on quantum evolution speed that accounts for decoherence effects and links it to quantum Fisher information.

Findings

Decomposition of quantum speed limit into three physical contributions.

Establishment of a trade-off between evolution speed and estimation precision.

Analytical bounds applicable to Markovian open quantum systems.

Abstract

We derive a new quantum speed limit (QSL) for open quantum systems governed by Markovian dynamics. By analyzing the time derivative of the Bures angle between the initial pure state and its time-evolved state, we obtain an analytically computable upper bound on the evolution speed that decomposes into three distinct physical contributions; coherent unitary dynamics, dissipative deformation, and a fluctuation term. Based on this structure, we establish a general inequality that connects the QSL to the Quantum Fisher information in the short-time regime. This result gives a fundamental trade-off between the distinguishability between speed and estimation precision, and clarifies how decoherence can both accelerate and constrain information acquisition.