  The phirotope is a complex generalization of the concept of chirotope in
oriented matroid theory. Our main goal in this work is to establish a link
between phirotopes, super p-branes and qubit theory. For this purpose we first
discuss maximally supersymmetric solutions of 11-dimensional supergravity from
the point of view of the oriented matroid theory. We also clarify a possible
connection between oriented matroid theory and supersymmetry via the
Grassmann-Pl\"ucker relations. These links are in turn useful for explaining
how our approach can be connected with qubit theory.
