Quantum Secret Sharing with error correction

TL;DR

This paper explores quantum secret sharing using five-qubit graph states with error correction, analyzing how different quantum codes recover from errors in noisy channels, especially when multiple qubits are disturbed.

Contribution

It introduces procedures for five, seven, and nine-qubit quantum error correction codes applied to secret sharing, detailing their error recovery capabilities under various noise conditions.

Findings

Five-qubit code allows error correction if only one qubit is disturbed.

Seven and nine-qubit codes extend error correction to more disturbed qubits.

Error correction effectiveness depends on the code used when multiple qubits are affected.

Abstract

We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes always allow error recovery if only one among the sents qubits is disturbed in the transmitting channel. However, if two qubits and more are disturbed, then the correction will depend on the used code.