Do single-shot projective readouts necessarily estimate the $T_1$ lifetime ?

Abstract

When single-shot qubit readout protocols are adapted for multilevel systems, theoretical $T_1$ lifetime calculations often fall short of capturing the experimental lifetime trends. We identify extrinsic population dynamics as the fundamental origin of this disparity, establishing that the lifetime estimates can, in certain operating regions, be distinct from the intrinsic $T_1$ time. We clarify these aspects with an integrated theory to address recent measurements [Nat. Nano, 20, 494, (2025)] on spin-valley states in bilayer graphene. While confirming that phonon and Johnson noise are the dominant intrinsic sources, we show that the inclusion of extrinsic factors provide the critical match to the experimental estimates. The extrinsic factors also effectuate violations of generalized Mathiessen's rules. With an improved handle on the design space, a revised readout protocol to estimate the $T_1$ lifetime of the valley qubit is proposed.