[Paper Review] A Quantum Bit Commitment Protocol Based on EPR States

M. Ardehali|ArXiv.org|May 26, 1995

Quantum Mechanics and Applications5 references4 citations

TL;DR

This paper proposes a quantum bit commitment protocol using Einstein-Podolsky-Rosen (EPR) entangled particle pairs, enabling secure commitment with current technology. It remains secure against cheating parties with unlimited computational power, provided the sender cannot store EPR particles indefinitely—offering a practical, efficient solution with tens of particles, though vulnerable if long-term storage is possible.

ABSTRACT

A protocol for quantum bit commitment is proposed. The protocol is feasible with present technology and is secure against cheaters with unlimited computing power as long as the sender does not have the technology to store an EPR particle for an arbitrarily long period of time. The protocol is very efficient, requiring only tens of particles.

Motivation & Objective

• To design a practical quantum bit commitment protocol that is secure against computationally unbounded adversaries.
• To ensure security under realistic physical constraints, particularly limiting the sender's ability to store entangled particles for long durations.
• To provide an efficient protocol requiring only tens of particles, suitable for implementation with existing quantum technology.
• To analyze the security limitations of the protocol when the sender gains the capability to store EPR particles indefinitely.
• To contribute to the foundational understanding of quantum commitment protocols in the context of entanglement and information locking.

Proposed method

• The protocol uses EPR entangled particle pairs prepared in a Bell state, shared between the sender and receiver.
• The sender commits to a bit by measuring her particle in a basis determined by the bit value, while the receiver measures his particle later.
• The protocol relies on quantum monogamy of entanglement: if the sender entangles her particle with a third system, it reduces the entanglement with the receiver’s particle.
• Security is based on the physical impossibility of storing an EPR particle indefinitely, which would allow the sender to later alter her commitment.
• The protocol is designed to be efficient, requiring only tens of EPR pairs for a single bit commitment.
• The protocol is analyzed under the assumption that the receiver is honest but the sender may cheat, and vice versa.

Experimental results

Research questions

• RQ1 Can a quantum bit commitment protocol be constructed using EPR states that is secure against unbounded computational power?
• RQ2 What physical limitations prevent a cheating sender from breaking the protocol?
• RQ3 How many EPR particles are required to achieve a secure and efficient commitment?
• RQ4 What happens to the protocol's security if the sender can store entangled particles for arbitrarily long times?
• RQ5 Can the protocol be implemented with current quantum technology?

Key findings

• The protocol is secure against cheating senders with unlimited computational power, provided they cannot store EPR particles for an arbitrarily long time.
• A cheating sender who can store EPR particles indefinitely can break the protocol by entangling her particle with a third system and later choosing her measurement basis to alter the commitment.
• The protocol requires only tens of EPR particles, making it efficient and feasible with current quantum technology.
• The security relies on the monogamy of entanglement: if the sender shares entanglement with an external system, it reduces the entanglement with the receiver’s particle.
• The protocol is vulnerable to attacks involving long-term quantum memory, highlighting a fundamental limitation in quantum bit commitment.
• The protocol is not secure in the standard model of quantum cryptography if the sender has access to a quantum memory of unbounded capacity.