  Investigations of quantum mechanical effects in macroscopic systems are of
great interest to shed light onto the question where and how the transition to
the classical world appears. It is also of practical relevance to determine if
a bath dephasing a qubit can be described classically or requires a quantum
mechanical treatment. We propose a measurement scheme to detect quantum
backaction via correlation measurements to answer this question for a bath
coupled to a single qubit. The presence of backaction leads to a dependence of
correlations of subsequent initialization-evolution-readout cycles on how the
qubit is manipulated in between. We compute the autocorrelation function for
both an instructive spin model and the realistic case of an electron spin
coupled to a bath of $10^6$ nuclear spins, as found in gated GaAs quantum dots,
and show that backaction from the qubit onto the nuclear spin bath should be
detectable even in such a large system.
