  We introduce grading on certain finite dimensional simple Lie superalgebras
of type $P(t)$ by elementary abelian 2-group. This grading gives rise to Pauli
matrices and is a far generalization of $(\mathbb Z_2\times \mathbb
Z_2)$-grading on Lie algebra of $(2\times 2)$-traceless matrices.We use this
grading for studying numerical invariants of polyomial identities of Lie
superalgebras. In particular, we compute graded PI-exponent corresponding to
Pauli grading.
