Probabilistic Quantum Teleportation

TL;DR

This paper establishes a unified condition for faithful probabilistic quantum teleportation of pure and mixed states, providing a practical method to determine teleportation success probability and measurement basis for partially entangled channels.

Contribution

It introduces a general relation $ ho_{q} ho_{m} = pI$ that describes conditions for faithful teleportation, unifying pure and mixed state cases, and explores invariance under unitary transformations.

Findings

Derived a universal condition for faithful teleportation.

Provided a procedure to find measurement basis and success probability.

Enhanced understanding of probabilistic teleportation with partially entangled channels.

Abstract

Teleporation with partially entangled quantum channel cannot achieve unit fidelity and unit probability. We show that the conditions for faithful teleportation of a pure state or a mixed state can be described by the same general relation $\rho_{q}\rho_{m} = pI$, where $\rho_{q}$ is the reduced density matrix of the quantum channel, $\rho_{m}$ is the reduced density matrix of the measurement basis, and $p$ is the probability of faithful teleportaion. We investigate the invariance of faithful teleportation conditions under unitary transformation. These results not only bring new insights to the probabilistic quantum teleportation theory, but also offer operational significance in that a simple procedure is provided to find out the faithful teleportaiton probability and the matching measurement basis for any partially entangled quantum channel.