  In this paper, we introduce a new measure of correlation for bipartite
quantum states. 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 $\alpha$-R\'enyi mutual information, and reduces to the trace
norm (total variation distance) for $\alpha=1$. We will prove some decoupling
type theorems in terms of this measure of correlation, and present some
applications in privacy amplification as well as in bounding the random coding
exponents. In particular, we establish a bound on the secrecy exponent of the
wiretap channel (under the total variation metric) in terms of the
$\alpha$-R\'enyi mutual information according to \emph{Csisz\'ar's proposal}.
