Quantum state concentration and classification of multipartite entanglement

Entanglement is a unique feature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we introduce a quantum state concentration scheme which decomposes the multipartite entangled state into a set of bipartite and tripartite entangled states. It is shown that the complexity of the entanglement induced by the large number of particles is transformed into the high dimensions of bipartite and tripartite entangled states for pure quantum systems. The results not only simplify the tedious work of verifying the (in)equivalence of multipartite entangled states, but also are instructive in the quantum many-body problem involving multipartite entanglement.

Figure 1

A 12-partite entangled state is first transformed into six tripartite states and one six-partite state: $({\mathrm{\Psi }}_{u_1},{\mathrm{\Psi }}_{u_2},...,{\mathrm{\Psi }}_{u_6},{\mathrm{\Omega }}_{j_1{j}_2\cdots j_6})$. Further rescaling may turn the 12-partite state into ten tripartite states and one bipartite state.