Quantum Fingerprints in Higher Order Correlators of a Spin Qubit

The spin of an electron in a semiconductor quantum dot represents a natural nanoscale solid state qubit. Coupling to nuclear spins leads to decoherence that limits the number of allowed quantum logic operations for this qubit. Traditional approach to characterize decoherence is to explore spin Relaxation and the spin echo, which are equivalent to the studies of the spins 2nd order time-correlator at various external conditions. Here we develop an alternative technique by showing that considerable information about dynamics can be obtained from direct measurements of higher than the 2nd order correlators, which to date have been hindered in semiconductor quantum dots. We show that such correlators are sensitive to pure quantum effects that cannot be explained within the classical framework, and which allow direct determination of ensemble and quantum dephasing times with only repeated projective measurements without the need for coherent spin control. Our method enables studies of pure quantum effects, including tests of the Leggett-Garg type inequalities that rule out local hidden variable interpretation of the spin qubit dynamics.