Generalized Smolin states and their properties

Four-qubit bound entangled Smolin states are generalized with help of the Hilbert-Schmidt formalism to any even number of qubits. They are shown to maximally violate simple correlation Bell inequalities and, as such, to reduce communication complexity, although they do not admit quantum security. They are also shown to serve for remote quantum information concentration, as in the case of the original four-qubit states. It is proven that the latter effect allows us to unlock some entanglement measures and classical correlations. Also the possibility of quantum secret sharing by the considered state is pointed out.

Figure 1

Network generating the Werner state.

Figure 2

Brief description of network generating the Werner state.

Figure 3

Network generating the noisy Smolin states.

Figure 4

Brief description of the network generating ${\varrho }_{2n}\left(p\right)$.

Figure 5

Networks generating the GSS states.