Full Frequency Back-Action Spectrum of a Single-Electron Transistor during Qubit Readout

We calculate the spectral density of voltage fluctuations in a single-electron transistor (SET), biased to operate in a transport mode where tunneling events are correlated due to Coulomb interaction. The whole spectrum from low frequency shot noise to quantum noise at frequencies comparable to the SET charging energy $(E_C/ħ)$ is considered. We discuss the back-action during readout of a charge qubit and conclude that single-shot readout is possible using the radio-frequency SET.