Device-Independent Quantum Key Distribution with Arbitrarily Small Nonlocality

Area of Science:

• Quantum Information Science
• Cryptography
• Quantum Computing

Background:

• Device-independent quantum key distribution (DIQKD) enables secure key establishment without trusting quantum devices.
• DIQKD relies on nonlocal correlations, but prior work showed nonlocality isn't always sufficient.
• The necessity of a minimum nonlocality threshold for DIQKD remained an open question.

Purpose of the Study:

• To investigate if a fundamental lower bound on nonlocality exists for DIQKD.
• To develop schemes for DIQKD using correlations close to the classical limit.
• To explore quantum correlations enabling simultaneous key and randomness generation.

Main Methods:

• Analysis of a family of Bell inequalities for self-testing maximally entangled states.
• Construction of DIQKD schemes utilizing specific nonlocal correlations.
• Examination of Clauser-Horne-Shimony-Holt (CHSH) values for these correlations.

Main Results:

• Demonstrated that no fundamental lower bound on nonlocality is required for DIQKD.
• Developed schemes achieving secure key distribution with correlations arbitrarily close to the local bound.
• Achieved maximum key rates (1 bit per entangled qubit) in some constructions.
• Identified quantum correlations yielding perfect key and randomness with minimal CHSH violation.

Conclusions:

• The findings remove the necessity for strong nonlocality in DIQKD, broadening its applicability.
• New DIQKD protocols can be realized using correlations near the classical threshold.
• The simultaneous generation of key and randomness opens avenues for advanced cryptographic protocols.