Randomness Amplification under Minimal Fundamental Assumptions on the Devices

Area of Science:

• Quantum Information Theory
• Cryptography
• Foundations of Quantum Mechanics

Background:

• Existing protocols for randomness amplification often require more than minimal conditions.
• The practical relevance of amplifying randomness from Santha-Vazirani sources under minimal assumptions was an open question.

Purpose of the Study:

• To develop a device-independent protocol for randomness amplification using only two non-signaling components.
• To determine if partial randomness, certified by Bell inequality violations, is sufficient for amplification.
• To prove the security of the protocol against general non-signaling adversaries.

Main Methods:

• Device-independent protocol construction using two non-signaling components.
• Utilizing partial randomness from Bell test violations.
• Employing a partial tomographic procedure on empirical statistics.
• Proving composable security against general non-signaling adversaries.

Main Results:

• A device-independent protocol for randomness amplification of Santha-Vazirani sources is presented.
• The protocol successfully amplifies any non-fully deterministic source into a fully random source.
• Constant noise rates are tolerated, and composable security is proven.
• Demonstrated that partial randomness from Bell tests can be leveraged for amplification.

Conclusions:

• The minimal conditions for randomness amplification are achieved using two non-signaling components.
• The protocol offers a practical and secure method for generating cryptographic random bits from weak sources.
• The findings advance the understanding of device-independent protocols and randomness certification.