We study the synchronization of dynamical systems induced by common additional external colored noise. In particular, we consider the special case that the external input noise is generated by a linear second-order differential equation forced by Gaussian white noise. So the frequency spectrum of this noise is not constant. In the case that noise-free dynamics is chaotic, we find examples where the synchronization is enhanced when the peak of the input noise is close to the peak of the noise-free dynamics in frequency space. In the case that noise-free dynamics is non-chaotic, we do not observe this phenomenon.

Secret key agreement is a procedure for agreeing on a secret key by exchanging messages over a public channel when a sender, a legitimate receiver (henceforth referred to as a receiver), and an eavesdropper have access to correlated sources. Maurer [6] defined secret key capacity, which is the least upper bound of the key generation rate of the secret key agreement, and presented an upper and a lower bound for the secret key capacity. The advantage distillation capacity is introduced and it is shown that this quantity equals to the secret key capacity. Naive information theoretical expressions of the secret key capacity and the advantage distillation capacity are also presented. An example of correlated sources, for which an analytic expression of the secret key capacity can be obtained, is also presented.