Teleportation of unknown qubit via Star type tripartite states

TL;DR

This paper demonstrates that certain tripartite $Star$-type states enable perfect quantum teleportation, challenging previous conjectures linking entanglement measures to teleportation capability, and shows that genuine tripartite entanglement is not essential.

Contribution

The study introduces $Star$-type tripartite states as effective teleportation channels and refutes the necessity of genuine tripartite entanglement for successful teleportation.

Findings

Perfect teleportation with $Star$ states confirmed.

Genuine tripartite entanglement not required for teleportation.

$Star$ states have $P_{max}=rac{1}{4}$ and Groverian entanglement $rac{ oot 3 rom rac{ ext{3}}{ ext{2}}}$.

Abstract

Eylee Jung \textit{et.al}\cite{jung2008} 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\cite{pati2006} have successfully executed perfect (standard) teleportation with non-prototype $W$ state. Aligned with Pati's protocol\cite{pati2006} 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.