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

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.