  The entanglement in a pure state of N qudits (d-dimensional distinguishable
quantum particles) can be characterised by specifying how entangled its
subsystems are. A generally mixed subsystem of m qudits is obtained by tracing
over the other N-m qudits. We examine the entanglement in the space of mixed
states of m qudits. We show that for a typical pure state of N qudits, its
subsystems smaller than N/3 qudits will have a positive partial transpose and
hence are separable or bound entangled. Additionally, our numerical results
show that the probability of finding entangled subsystems smaller than N/3
falls exponentially in the dimension of the Hilbert space. The bulk of pure
state Hilbert space thus consists of highly entangled states with multipartite
entanglement encompassing at least a third of the qudits in the pure state.
