In the case of a linear symplectic map A of the 2d-torus, semiclassical
measures are A-invariant probability measures associated to sequences of high
energy quantum states. Our main result is an explicit lower bound on the
entropy of any semiclassical measure of a given quantizable matrix A in
Sp(2d,Z). In particular, our result implies that if A has an eigenvalue outside
the unit circle, then a semiclassical measure cannot be carried by a closed
orbit of A.