Classical Bound on the Fisher Information Rate of a Dephasing-Enhanced Quantum Neuron

Abstract

Dephasing can sharpen the activation of a dissipative quantum neuron, but a stationary response does not determine how much input information its output delivers per unit time. For a single qubit with partial-reset updates at rate $\nu$, we derive the threshold response bandwidth and the exact local Fisher information rate of the complete record from repeated projective readouts, including their backaction. Near the activation threshold, the rate obeys $\mathcal{R}\le \nu (1-s)(1+s{)}^2/2\le 16\nu /27$, where $s$ is the retained amplitude of each update. For every fixed finite Markovian dephasing rate, optimization over the readout interval and $s$ gives the same supremum, approached at $s=1/3$ with arbitrarily rapid ideal readout. A finite measurement dead time instead selects a finite optimal interval, which we obtain by a dimensionless two-parameter optimization. The ideal bound is saturated by a classical two-state jump process: quantum coherence changes finite-cadence performance but cannot raise the optimized bound. These results separate noise-enhanced activation from the operational information throughput of a quantum neuron and provide a hardware-aware benchmark for finite-time quantum neural processing.