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

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.

9 pages, no figure, V2: 11 pages. Prove that two general 3-qubit states, which allow the perfect quantum teleportation, have $P_{max}=1/2$

References in corpus (1)

• Geometric Measure of Entanglement and Shared Quantum States