  We study the dispersive readout of a qubit in the ultimate limit of a
single-photon probe. The use of a single-photon probe avoids the errors due to
nonorthogonality of coherent states. A photodetector is used in the scheme we
consider. The dynamics of the system is studied using the Heisenberg-Langevin
equations. We treat the counter-rotating terms in the Hamiltonian
perturbatively, which leads to the Bloch-Siegert shift in the resonator
frequency. It is shown how this can improve the readout. The theory of photon
transport through the qubit and the resonator it couples to is provided while
taking the effect of the counter-rotating terms into account. To calculate the
readout contrast, we use two approaches. The first one neglects the qubit
relaxation and allows us to derive a compact expression for the contrast. Also,
we obtain simple estimates for the system parameters to maximize the contrast.
The second approach accounts for the qubit relaxation, which allows us to
further improve the contrast. We demonstrate that for a readout time of
1$\mu$s, a contrast of more than 75% can be achieved for an ideal detector and
single-photon source.
