Teleportation of unknown qubit via Star-type tripartite states

Eylee Jung et.al[1] had conjectured that \(P_{max}=\frac{1}{2}\) is a necessary and sufficient condition for the perfect two-party teleportation, and consequently, the Groverian measure of entanglement for the entanglement resource must be \(\frac{1}{\sqrt{2}}\). It is also known that prototype W state is not useful for standard teleportation. Agrawal and Pati[2] have successfully executed perfect (standard) teleportation with non-prototype W state. Aligned with the protocol mentioned in[2], we have considered here Star type tripartite states and have shown that perfect teleportation is suitable with such states. Moreover, we have taken the linear superposition of non-prototype W state and its spin-flipped version and shown that it belongs to Star class. Also, standard teleportation is possible with these states. It is observed that genuine tripartite entanglement is not necessary requirement for a state to be used as a channel for successful standard teleportation. We have also shown that these Star class states are \(P_{max}=\frac{1}{4}\) states and their Groverian entanglement is \(\frac{\sqrt{3}}{2}\), thus concluding that Jung conjecture is not a necessary condition.