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.
Surya Sekhar Roy (Fri,) studied this question.