Secrecy in Prepare-and-Measure Clauser-Horne-Shimony-Holt Tests with a Qubit Bound

Area of Science:

• Quantum Information Science
• Quantum Cryptography
• Foundations of Quantum Mechanics

Background:

• Device-independent (DI) quantum key distribution (QKD) security relies on Bell inequality violation.
• DI-QKD typically requires entangled states, limiting practical implementations.
• Entanglement-based DI-QKD security proofs often use a specific lower bound on min entropy related to the Clauser-Horne-Shimony-Holt (CHSH) Bell correlator.

Purpose of the Study:

• To demonstrate that a known security bound for entanglement-based DI-QKD also applies to prepare-and-measure protocols.
• To relax the reliance on entanglement for certain DI-QKD security proofs.
• To provide a more accessible security framework for DI-QKD.

Main Methods:

• Mathematical proof establishing a connection between Bell inequality violation and min entropy in a prepare-and-measure setting.
• Analysis of the Clauser-Horne-Shimony-Holt (CHSH) Bell correlator in the context of prepare-and-measure protocols.
• Utilizing the assumption of a two-dimensional Hilbert space for the quantum source.

Main Results:

• A tight lower bound on min entropy in terms of the CHSH Bell correlator is proven to hold for prepare-and-measure protocols.
• This bound, previously used in entanglement-based DI-QKD security proofs, is now shown to be applicable under weaker assumptions.
• The security analysis of DI-QKD can be extended to protocols not requiring explicit entanglement distribution.

Conclusions:

• The security of device-independent quantum key distribution can be established using prepare-and-measure protocols with minimal assumptions.
• This finding simplifies the theoretical security analysis of DI-QKD systems.
• The established bound offers a pathway to more practical and secure quantum key distribution implementations.