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Two signatures of quantum effects on radiation reaction in the collision of a GeV electron beam with a high intensity ( }3\times 1020~\text{W}~\text{cm}-2$) laser pulse have been considered. We show that the decrease in the average energy of the electron beam may be used to measure the Gaunt factor for synchrotron emission. We derive an equation for the evolution of the variance in the energy of the electron beam in the quantum regime, i.e. quantum efficiency parameter . We show that the evolution of the variance may be used as a direct measure of the quantum stochasticity of the radiation reaction and determine the parameter regime where this is observable. For example, stochastic emission results in a 25 % increase in the standard deviation of the energy spectrum of a GeV electron beam, 1 fs after it collides with a laser pulse of intensity 21~\text{W}~\text{cm}-2$ . This effect should therefore be measurable using current high-intensity laser systems.