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We study how single-qubit dispersive readout works alongside two qubitcoupling. To make calculations analytically tractable, we use a simplifiedmodel which retains core characteristics of but is discretised compared todispersive homodyne detection. We show how measurement speed and powerdetermine what information about the qubit(s) is accessed. Specifically we findthe basis the measurement is closest to projecting onto. Compared to the basisgates are applied in, this measurement basis is modified by the presence ofphotons in the readout resonator.

What is measured when a qubit measurement is performed on a multi-qubit chip?