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arXiv · 2601.12475

Stochastic Quantum Information Geometry and Speed Limits at the Trajectory Level

Pedro B. Melo·Pedro V. Paraguassú·Sílvio M. Duarte Queirós·Fernando Iemini·Mauro Paternostro·Welles A. M. Morgado
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Abstract

In quantum metrology, precision is typically characterized by an ensemble-averaged quantity, the quantum Fisher information (QFI), which averages over the fluctuations of individual measurement records. Here we introduce the conditional quantum Fisher information (CQFI), a trajectory-level version of the QFI that generalizes the classical stochastic Fisher information to the quantum domain. Defined through the symmetric logarithmic derivative and conditioned on a measurement outcome, the CQFI is a random variable whose average recovers the QFI. Using it, we derive a trajectory-level quantum speed limit, illustrated by the quantum-jump unraveling of a driven thermal qubit. Moreover, the CQFI decomposes into incoherent (population) and coherent (basis-rotation) contributions, together with an interference cross-term. This cross-term vanishes on average but can take negative values along single trajectories, providing a local witness of destructive interference between classical and quantum information channels.

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Pedro B. Melo, Pedro V. Paraguassú, Sílvio M. Duarte Queirós, Fernando Iemini, Mauro Paternostro, Welles A. M. Morgado. 2026-01-18. Stochastic Quantum Information Geometry and Speed Limits at the Trajectory Level. https://arxiv.org/abs/2601.12475

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