Encoding-aware Fisher diagnostics in open quantum systems: Separating Backflow from Process-Parameter Readability

Fisher information is widely used as a diagnostic in quantum sensing, readout, and open-system dynamics, but its temporal growth does not always have the same physical meaning. This preprint introduces an encoding-aware separation between different Fisher layers in open quantum systems. It distinguishes whether the estimated parameter is encoded in the input state, written into the output by the dynamical channel, or accessed through a fixed measurement record. For input-encoded parameters propagated by parameter-independent CP-divisible dynamics, a revival of optimized quantum Fisher information can be interpreted as a candidate signal of information backflow. For channel-encoded parameters, however, Fisher information may grow even under a Markovian semigroup, because the dynamics progressively imprints the process parameter into the output state. Fixed-readout Fisher information forms a third layer: it is experimentally useful, but its interpretation depends on the chosen analyzer and measurement geometry. The paper develops this distinction as a practical interpretation rule for quantum-information diagnostics. Dephasing, amplitude-damping, and two-qubit X-state examples show that Fisher readability, coherence, concurrence, and complementarity can coincide in calibrated sectors but separate in general. In particular, there are regimes where phase Fisher readability remains nonzero even after concurrence has vanished. The main message is that Fisher growth becomes causally meaningful only after the encoding, dynamical map, and readout layer have been specified.