  Contact has been well established as an important quantity to govern dilute
quantum systems, in which the pairwise correlation at short distance traces a
broad range of thermodynamic properties. So far, studies have been focusing on
contact in individual angular momentum channels. Here, we point out that, to
have a complete description of the pairwise correlation in a general dilute
quantum systems, contact should be defined as a matrix. Whereas the diagonal
terms of such matrix include contact of all partial wave scatterings, the
off-diagonal terms, which elude previous studies in the literature,
characterise the coherence of the asymptotic pairwise wavefunction in the
angular momentum space and determine important thermodynamic quantities
including the momentum distribution. Contact matrix allows physicists to access
unexplored connections between short-range correlations and macroscopic quantum
phenomena. As an example, we show the direct connection between contact matrix
and order parameters of a superfluid with mixed partial waves.
