Perfect Quantum Teleportation and Superdense coding with $P_{max} = 1/2$ states

TL;DR

This paper proposes a conjecture linking perfect quantum teleportation to a specific Groverian entanglement measure and verifies it through analysis of certain quantum states allowing perfect teleportation and superdense coding.

Contribution

It introduces a conjecture that perfect teleportation requires Groverian entanglement of 1/√2 and provides explicit examples supporting this claim.

Findings

States with Groverian measure 1/√2 enable perfect teleportation.

The conjecture is supported by analyzing specific quantum states.

Explicit calculations confirm the link between entanglement measure and teleportation perfection.

Abstract

We conjecture that criterion for perfect quantum teleportation is that the Groverian entanglement of the entanglement resource is $1/\sqrt{2}$. In order to examine the validity of our conjecture we analyze the quantum teleportation and superdense coding with $|\Phi> = (1/\sqrt{2}) (|00q_1> + |11q_2>)$, where $|q_1>$ and $|q_2>$ are arbitrary normalized single qubit states. It is shown explicitly that $|\Phi>$ allows perfect two-party quantum teleportation and superdense coding scenario. Next we compute the Groverian measures for $|\psi>=\sqrt{1/2 - b^2}|100>+b |010>+a|001> +\sqrt{1/2-a^2}|111>$ and $|\tilde{\psi}>=a|000>+b|010>+\sqrt{1/2 - (a^2+b^2)}|100> + (1/\sqrt{2}) |111>$, which also allow the perfect quantum teleportation. It is shown that both states have $1/\sqrt{2}$ Groverian entanglement measure, which strongly supports that our conjecture is valid.