Maximally entangled states of four nonbinary particles
Mario Gaeta, A. B. Klimov, Jay Lawrence · Physical Review A · 2015
Systems of four nonbinary particles, with each particle having $d\ensuremath{\ge}3$ 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 Greenberger-Horne-Zeilinger (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 also 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 prime $d\ensuremath{\ge}3$.