[Paper Review] Comment on Quantum teleportation and information splitting via four-qubit cluster state and a Bell state

Meiling Zhang, Sha Shi+3 more|arXiv (Cornell University)|Jul 31, 2018

Quantum Information and Cryptography1 references3 citations

TL;DR

This paper critiques a previously proposed quantum teleportation protocol using a four-qubit cluster state and a Bell state, arguing it fails to enable repeatable teleportation without copying the original state. The authors propose a modified protocol using unitary operations and Z-basis measurements, ensuring the original state remains with the sender if teleportation fails, thus enabling repeated attempts using fresh entangled channels with high success probability approaching 1 as trials increase.

ABSTRACT

We study the quantum controlled and probabilistic teleportation protocol via a four-cluster state (Front. Phys. (2017) 12: 120306). The protocol cannot achieve the goal that if the teleportation fails, it can be repeated without copies of the teleported state. And the reason is that all the information of the teleported state shifts to the receiver's particle after Bell measurement and the information cannot shift back to the sender without other entangled states. To realize the claimed goal, a new quantum controlled and probabilistic teleportation protocol using the same four-cluster state is presented. Because no information of the teleported stated is lost during the whole teleportation process, the teleportation process can be repeated until the teleportation success.

Motivation & Objective

• To identify a fundamental flaw in Ramírez et al.'s 2017 protocol that prevents repeated teleportation without copying the original state.
• To address the issue that all information about the teleported state is irreversibly transferred to the receiver after Bell measurements.
• To design a new controlled and probabilistic teleportation protocol that preserves the original state with the sender upon failure, enabling repeated attempts.
• To demonstrate analytically and via simulation that the success probability approaches 1 with increasing number of trials or higher success probability per trial.

Proposed method

• Replace Bell measurements with a sequence of unitary operations and Z-basis measurements on the sender’s qubits to preserve the original state information.
• Use auxiliary qubits and POVMs to probabilistically verify teleportation success while keeping the original state intact if failure occurs.
• Apply Pauli operators (σX, σZ) conditionally based on measurement outcomes to correct the receiver’s state when successful.
• Model the teleportation process as a geometric distribution with success probability p = 2(|α|² + |β|²), enabling repeated trials with new entangled channels.
• Simulate the total success probability Pr(X ≤ N) = 1 − (1 − p)^N as a function of p and N to evaluate scalability and convergence.
• Analyze the state evolution after each measurement step, showing that the original state remains in the sender’s possession when the auxiliary qubit collapses to |1⟩.

Experimental results

Research questions

• RQ1 Can the original quantum state be preserved with the sender after a failed teleportation attempt in a controlled, probabilistic teleportation scheme?
• RQ2 Does replacing Bell measurements with Z-basis measurements and unitary operations allow for repeatable teleportation without requiring a copy of the original state?
• RQ3 What is the success probability of the proposed protocol, and how does it scale with the number of repeated attempts?
• RQ4 Can the protocol achieve near-deterministic teleportation by increasing the number of trials or the per-trial success probability?

Key findings

• The original protocol by Ramírez et al. fails to allow repeated teleportation without copying the state, as all information is lost to the receiver after Bell measurement.
• The proposed protocol ensures the original state remains with the sender if teleportation fails, enabling repeated attempts using new entangled channels.
• The success probability of teleporting the unknown state approaches 1 as the number of trials N increases, especially when N ≥ 50.
• The success probability also increases significantly with higher per-trial success probability p, reaching near-unity when p ≥ 0.3.
• The total success probability is modeled as Pr(X ≤ N) = 1 − (1 − p)^N, showing rapid convergence to 1 for large N or large p.
• The protocol maintains information integrity throughout the process, with the sender retaining the original state in the failure case, enabling reliable and repeatable teleportation.