  Systems of four nonbinary particles, each having three or more internal
states, exhibit maximally entangled states that are inaccessible to four
qubits. This breaks the pattern of two- and three-particle systems, in which
the existing graph states are equally accessible to binary and nonbinary
systems alike. We compare the entanglement properties of these special states
(called P-states) with those of the more familiar GHZ and cluster states
accessible to qubits. The comparison includes familiar entanglement measures,
the "steering" of states by projective measurements, and the probability that
two such measurements, chosen at random, leave the remaining particles in a
Bell state. These comparisons demonstrate not only that P-state entanglement is
stronger than the other types, but that it is maximal in a well-defined sense.
We prove that GHZ, cluster, and P-states represent all possible entanglement
classes of four-particle graph states with a prime number (>2) of states per
particle.

Quantum Physics