Quantum Secret Sharing

Quantum Secret Sharing

1 December, 1998 | Mark Hillery¹, Vladimír Bužek², and André Berthiaume³
Quantum secret sharing is a method to split a message into parts such that no subset of parts can reconstruct the message, but the entire set can. This is achieved using GHZ (Greenberger-Horne-Zeilinger) states, which are maximally entangled three-particle states. In the quantum case, an eavesdropper's presence introduces errors, allowing detection. GHZ states can also split quantum information into two parts, requiring both to reconstruct the original qubit. The paper introduces a quantum secret sharing protocol using GHZ states. Alice, Bob, and Charlie each have one particle from a GHZ triplet. They randomly choose measurement directions (x or y) and announce their choices. By combining their results, they can determine Alice's measurement outcome, establishing a shared key. This allows Alice to securely send her message. The protocol also addresses eavesdropping. If an eavesdropper, like Bob or Charlie, tries to intercept the particles, they introduce errors that can be detected by Alice, Bob, and Charlie. The paper shows that if an eavesdropper entangles an ancilla with the GHZ state, it introduces errors, allowing detection. The protocol is extended to four parties using a four-particle GHZ state. Each party measures their particle in either the x or y basis. By combining their results, they can determine Alice's measurement outcome. This ensures that only all three parties can reconstruct the original information. The paper concludes that GHZ states can split information securely, both classically and quantum mechanically. In quantum information, a qubit is split into two parts, requiring both to reconstruct the original. This method is more efficient than classical secret sharing and quantum cryptography, as it uses entanglement to substitute for classical communication. The protocol is secure against eavesdropping and cheating, ensuring information remains protected.Quantum secret sharing is a method to split a message into parts such that no subset of parts can reconstruct the message, but the entire set can. This is achieved using GHZ (Greenberger-Horne-Zeilinger) states, which are maximally entangled three-particle states. In the quantum case, an eavesdropper's presence introduces errors, allowing detection. GHZ states can also split quantum information into two parts, requiring both to reconstruct the original qubit. The paper introduces a quantum secret sharing protocol using GHZ states. Alice, Bob, and Charlie each have one particle from a GHZ triplet. They randomly choose measurement directions (x or y) and announce their choices. By combining their results, they can determine Alice's measurement outcome, establishing a shared key. This allows Alice to securely send her message. The protocol also addresses eavesdropping. If an eavesdropper, like Bob or Charlie, tries to intercept the particles, they introduce errors that can be detected by Alice, Bob, and Charlie. The paper shows that if an eavesdropper entangles an ancilla with the GHZ state, it introduces errors, allowing detection. The protocol is extended to four parties using a four-particle GHZ state. Each party measures their particle in either the x or y basis. By combining their results, they can determine Alice's measurement outcome. This ensures that only all three parties can reconstruct the original information. The paper concludes that GHZ states can split information securely, both classically and quantum mechanically. In quantum information, a qubit is split into two parts, requiring both to reconstruct the original. This method is more efficient than classical secret sharing and quantum cryptography, as it uses entanglement to substitute for classical communication. The protocol is secure against eavesdropping and cheating, ensuring information remains protected.
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Understanding Quantum secret sharing