Multipartite fully nonlocal quantum states

We present a general method for characterizing the quantum correlations obtained after local measurements on multipartite systems. Sufficient conditions for a quantum system to be fully nonlocal according to a given partition, as well as being (genuinely) multipartite fully nonlocal, are derived. These conditions allow us to identify all completely connected graph states as multipartite fully nonlocal quantum states. Moreover, we show that this feature can also be observed in mixed states: the tensor product of five copies of the Smolin state, a biseparable and bound entangled state, is multipartite fully nonlocal.

Figure 1

Local measurements are performed on parties $A_2\dots A_{m-1}$ of an $m$-partite state $\rho$. If for every outcome of this partial measurement, $A_1$ and $A_m$ share a maximally entangled state, $\rho$ has $p_L^{\mathcal{A}:\mathcal{B}}=0$ (Theorem 1). If it holds for any possible bipartition, the state $\rho$ is multipartite fully nonlocal, $p_{\mathrm{NS}}=1$ (Theorem 2).