Comparison of the distributions of classical and adaptively aligned EEG power spectra

The distributions of eyes-closed resting electroencephalography (EEG) power spectra and their residuals were described and compared using classically averaged and adaptively aligned averaged spectra. Four minutes of eyes-closed resting EEG was available from 69 participants. Spectra were calculated with 0.5-Hz resolution and were analyzed at this level. It was shown that power in the individual 0.5 Hz frequency bins can be considered normally distributed when as few as three or four 2-second epochs of EEG are used in the average. A similar result holds for the residuals. Power at the peak Alpha frequency has quite different statistical behaviour to power at other frequencies and it is considered that power at peak Alpha represents a relatively individuated process that is best measured through aligned averaging. Previous analyses of contrasts in upper and lower alpha bands may be explained in terms of the variability or distribution of the peak Alpha frequency itself.

Noise in detection of qubit states using a quantum point contact

We present a model for detection of the states of a coupled quantum dots (qubit) by a quantum point contact. Most proposals for measurements of states of quantum systems are idealized. However in a real laboratory the measurements cannot be perfect due to practical devices and circuits. The models using ideal devices are not sufficient for describing the detection information of the states of the quantum systems. Our model therefore includes the extension to a non-ideal measurement device case using an equivalent circuit. We derive a quantum trajectory that describes the stochastic evolution of the state of the system of the qubit and the measuring device. We calculate the noise power spectrum of tunnelling events in an ideal and a non-ideal quantum point contact measurement respectively. We found that, for the strong coupling case it is difficult to obtain information of the quantum processes in the qubit by measurements using a non-ideal quantum point contact. The noise spectra can also be used to estimate the limits of applicability of the ideal model.