Target-Variance Quantum Speed Limits from Projective Fidelity Reduction

Quantum state readout on many experimental platforms is performed through a single projective measurement channel rather than full quantum state tomography. We derive a detector-conditioned quantum speed limit that constrains the minimum time for the projective fidelity [Formula: see text] to reach a prescribed discrimination threshold: [Formula: see text] where [Formula: see text] is the Bures angle and [Formula: see text] is the energy standard deviation of the fixed target state. This bound, valid for both pure and mixed states under unitary dynamics, expresses the speed constraint in terms of a time-independent quantity determined entirely by the Hamiltonian and the detector projector, rather than the evolving-state variance appearing in standard Mandelstam–Tamm-type bounds. We further show that the resulting bound is structurally distinct from standard Mandelstam–Tamm-type bounds based on evolving-state variance. The bound exhibits commuting-sector invariance, suppressing Hamiltonian components that are energetically large but detection-irrelevant. Exact diagonalization of the transverse-field Ising model for [Formula: see text] spins confirms asymptotic separation between the bounds in the strong-interaction regime. The framework provides a detector-conditioned lower bound for rank-1 projective detection dynamics, applicable to superconducting qubit readout, trapped-ion fluorescence detection, and stabilizer syndrome monitoring. The construction is particularly relevant for architectures in which experimentally accessible information is restricted to a small set of projective readout channels rather than full-state tomography.