Probabilistic Quantum Teleportation via 3-Qubit Non-Maximally Entangled GHZ State by Repeated Generalized Measurements

TL;DR

This paper presents a probabilistic quantum teleportation scheme using repeated generalized Bell state measurements on a 3-qubit non-maximally entangled GHZ state, achieving near-certain success with multiple attempts.

Contribution

It introduces a novel repeated measurement protocol for probabilistic teleportation with analytical success probability expressions linked to entanglement.

Findings

Success probability increases with repeated GBSM attempts.

Success probability converges to unity as the number of repetitions increases.

Analytical expressions relate success probability to bipartite concurrence.

Abstract

We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of $\sigma_{x}$. Both these measurement outcomes are communicated to Bob classically, which helps him to perform a suitable unitary transformation on qubit 3 to recover the information state. On the other hand, if failure is obtained, the next attempt of GBSM is performed on qubits 0 and 2. This process of repeating GBSM on alternate pair of qubits may continue until perfect teleportation with unit fidelity is achieved. We have obtained analytical expressions for success probability up to three repetitions of GBSM. The success probability is shown to be a polynomial function of bipartite concurrence of the NME resource. The variation of success probability with the bipartite concurrence has been plotted which shows the convergence of success probability to unity with GBSM repetitions.