Global Entanglement in Multiparticle Systems

We define a polynomial measure of multiparticle entanglement which is scalable, i.e., which applies to any number of spin1 2 particles. By evaluating it for three particle states, for eigenstates of the one dimensional Heisenberg antiferromagnet and on quantum error correcting code subspaces, we illustrate the extent to which it quantifies global entanglement. We also apply it to track the evolution of entanglement during a quantum computation. 2001 Physics and Astronomy Classification Scheme: 03.65.Ud, 05.30.-d, 03.67.Lx. 2000 American Mathematical Society Subject Classification: 81P68, 81R05.