Can observed randomness be certified to be fully intrinsic?

Area of Science:

• Quantum Information Science
• Foundations of Quantum Mechanics
• Information Theory

Background:

• Observed randomness in systems arises from apparent (ignorance-based) or intrinsic (fundamental) sources.
• Classical systems exhibit only apparent randomness, while quantum systems may possess intrinsic randomness.
• Understanding the origin of randomness is crucial for quantum information processing and fundamental physics.

Purpose of the Study:

• To demonstrate quantum processes where all observed randomness is intrinsically quantum.
• To establish minimal assumptions required for intrinsic quantum randomness.
• To explore the phenomenon of randomness amplification in quantum systems.

Main Methods:

• Utilizing the no-signaling principle, a fundamental constraint in quantum mechanics.
• Assuming an arbitrary, non-absolute lack of freedom of choice for experimental settings.
• Analyzing finite quantum scenarios involving multiple parties and dichotomic measurements.

Main Results:

• Quantum predictions cannot be fully explained by classical hidden variables even in simple finite scenarios (e.g., three parties, two measurements).
• The observed randomness in these quantum processes tends towards a perfect random bit as the number of parties increases.
• An explicit process demonstrating full randomness amplification is defined.

Conclusions:

• Quantum mechanics inherently supports intrinsic randomness, distinct from classical apparent randomness.
• The no-signaling principle and limited freedom of choice are sufficient to demonstrate genuine quantum randomness.
• Quantum systems offer a pathway to generate high-quality random numbers through randomness amplification, with significant implications for cryptography and computation.