Multiparticle entanglement and its applications to cryptography

Entanglement between three or more parties exhibits a realm of properties u nknown to two-party states. Bipartite states are easily classified using th e Schmidt decomposition. The Schmidt coefficients of a bipartite pure state encompass all the nonlocal properties of the state and can be "seen" by lo oking at one party's density matrix only. Pure states of three and more par ties, however, lack such a simple form. They have more invariants under loc al unitary transformations than any one party can ''see'' on their subsyste m. These ''hidden nonlocalities" will allow;us to exhibit a class of multip artite states that cannot be distinguished from each other by any party. Ge neralizing a result of Bennett, Popescu, Rohrlich, Smolin, and Thapliyal, a nd using a recent result by Nielsen, we will show that these states cannot be transformed into each other by local actions and classical communication . Furthermore, we will use an orthogonal subset of such states to hint at a pplications to cryptography and illustrate an extension to quantum secret s haring [using recently suggested ((n.k))-threshold schemes]. [S1050-2947(99 )01408-0].