[Paper Review] A simple unconditionally secure quantum bit commitment protocol via quantum teleportation

Horace P. Yuen|ArXiv.org|May 23, 2003

Quantum Information and Cryptography3 citations

TL;DR

This paper proposes a novel quantum bit commitment protocol (QBC5) that achieves unconditional security using quantum teleportation and classical information exchange. By committing a Bell measurement outcome and revealing the quantum state at opening, the protocol evades the standard impossibility proof by breaking the entanglement cheating mechanism through teleportation-induced control over measurement outcomes.

ABSTRACT

By using local quantum teleportation of a fixed state to one qubit of an entangled pair sent from the other party, it is shown how one party can commit a bit with only classical information as evidence that results in an unconditionally secure protocol. The well-known ``impossibility proof'' does not cover such protocols due to its different commitment and opening prescriptions, which necessitate actual quantum measurements among different possible systems that cannot be entangled as a consequence.

Motivation & Objective

• To address the long-standing belief that unconditionally secure quantum bit commitment is impossible due to entanglement cheating.
• To identify and correct gaps in the standard 'impossibility proof' of quantum bit commitment (QBC).
• To design a protocol that remains secure under the full framework of quantum mechanics without relying on external constraints like relativity.
• To demonstrate that classical information commitment via teleportation can achieve unconditionally secure bit commitment.
• To provide a security proof for a new class of protocols (Type 5 QBC) that differ fundamentally from those covered by the standard impossibility result.

Proposed method

• The protocol uses two-way quantum and classical communication, with Babe preparing entangled qubit pairs and applying private unitaries.
• Adam performs quantum teleportation of a known state (|0⟩ or |1⟩) from his ancilla to one qubit of the entangled pair.
• He commits the Bell-basis measurement result on the remaining qubit and a third system, sending only classical information as evidence.
• At opening, Adam sends back the teleported state and the remaining entangled pairs for verification via projection measurements.
• The protocol’s security relies on the fact that teleportation prevents Adam from entangling his opening strategies, breaking the entanglement cheating path.
• A game-theoretic framework is used to model cheating detection, with probabilistic checks and repetition to drive cheating probability to zero.

Experimental results

Research questions

• RQ1 Can unconditionally secure quantum bit commitment be achieved despite the standard impossibility proof?
• RQ2 What structural differences between this protocol and previous QBC schemes prevent entanglement cheating?
• RQ3 How does the use of quantum teleportation alter the security properties of bit commitment protocols?
• RQ4 Can classical information commitment, combined with quantum state exchange at opening, ensure both concealing and binding properties?
• RQ5 What role does the measurement outcome commitment play in evading the assumptions of the impossibility proof?

Key findings

• The protocol QBC5 is ε-concealing and can be extended to an ε-binding protocol through sequential repetition.
• The impossibility proof does not apply to this protocol because it uses a reversed commitment structure: measurement result is committed, and the quantum state is revealed at opening.
• Cheating by Adam is bounded away from perfect success; his optimal cheating probability P̄cA is strictly less than 1 due to the constraints of teleportation and measurement control.
• The protocol remains secure under a game-theoretic model where repeated checks drive the cheating probability P_C to zero as the number of trials increases.
• Even without penalties, the cheating probability can be made arbitrarily small by increasing the number of trials and adjusting the acceptance probability.
• The protocol's security is maintained even when the cheating party attempts to entangle states, due to the structure of the teleportation and measurement process.