In this paper, a new measure of correlation is introduced. This measure depends on a parameter alpha, and is defined in terms of vector-valued L-p norms. The measure is within a constant of the exponential of alpha-Renyi mutual information, and reduces to the trace norm (total variation distance) for alpha = 1. We provide some properties and applications of this measure of correlation. In particular, we establish a bound on the secrecy exponent of the wiretap channel (under the total variation metric) in terms of the alpha-Renyi mutual information according to Csiszar's proposal.