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 /∞) 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.