On a relation between the high and low frequency noise

Low-frequency (1/f) noise dominates the decoherence in most superconducting qubits. Thus it is very important to understand its origin and properties. Recently, coherent two-level systems have been observed in Josephson junctions [1]. These systems influence strongly qubits' dynamics at high ($\sim$ 10 GHz) frequencies. In addition, recent experiments [2] indicate a connection between the high- and low-frequency noise. In this work we note that an ensemble of coherent two-level systems produces simultaneously high- and low-frequency noise. The relation between these two contributions depends on the statistical properties of the ensemble. We analyze several possible distribution functions and relate the results to the known experimental facts. We also note that a similar relation holds for ensembles of many-level fluctuators with discrete spectrum. [1] R.W. Simmonds et al., Phys. Rev. Lett. 93, 035301 (2004) [2] O. Astafiev et al., cond-mat/0411216 (2004)