True randomness from realistic quantum devices (1311.4547v1)

Abstract: Even if the output of a Random Number Generator (RNG) is perfectly uniformly distributed, it may be correlated to pre-existing information and therefore be predictable. Statistical tests are thus not sufficient to guarantee that an RNG is usable for applications, e.g., in cryptography or gambling, where unpredictability is important. To enable such applications a stronger notion of randomness, termed "true randomness", is required, which includes independence from prior information. Quantum systems are particularly suitable for true randomness generation, as their unpredictability can be proved based on physical principles. Practical implementations of Quantum RNGs (QRNGs) are however always subject to noise, i.e., influences which are not fully controlled. This reduces the quality of the raw randomness generated by the device, making it necessary to post-process it. Here we provide a framework to analyse realistic QRNGs and to determine the post-processing that is necessary to turn their raw output into true randomness.

• The paper establishes a novel framework for evaluating randomness in noisy quantum devices by modeling them as mixed states with POVMs.
• The study reveals how side information and classical noise affect quantum random number generators and advocates two-universal hashing to remove biases.
• The research offers critical insights for enhancing cryptographic security by setting robust standards for true randomness extraction and QRNG design.

Analysis of "True randomness from realistic quantum devices"

The paper "True randomness from realistic quantum devices" by Frauchiger, Renner, and Troyer provides a comprehensive exploration of randomness generation, specifically focusing on Quantum Random Number Generators (QRNGs). They examine how these devices can be utilized to produce "true" randomness, which is essential for applications requiring unpredictable and uncorrelated random numbers, such as in cryptographic systems.

Concept of True Randomness

A key argument presented is that the output of an RNG may appear uniformly random from a statistical perspective, yet still be predictable when correlated with pre-existing information. This insight underscores the limitation of relying solely on statistical tests for randomness verification. The authors advocate a more stringent criterion—termed "true randomness"—which demands that generated numbers are both uniformly distributed and independent of any previously available information.

Quantum Systems as a Basis for Randomness

Quantum systems offer inherent unpredictability due to their probabilistic nature, making them suitable for true randomness generation. The paper elaborates on how measurements of quantum states can yield outcomes that adhere to the defined notion of true randomness. But practical implementations of QRNGs often introduce noise and imperfections, necessitating additional steps to distill true randomness from the raw data.

Framework for Analyzing QRNGs

The authors propose a novel framework to evaluate the randomness quality of QRNG outputs. This involves modeling QRNGs as quantum systems described by mixed states and POVMs (Positive Operator-Valued Measures), thus capturing more realistic scenarios where noise affects the randomness. The framework highlights the need for post-processing, specifically using two-universal hashing, to eliminate biases and dependencies introduced by noise.

Side Information and Classical Noise Models

To reconcile the theoretical model with practical realities, the paper considers side information—any details available that could correlate with or predict the RNG's output. Importantly, the proposed framework accommodates an analysis of these influences through a generalized model of classical noise that operates alongside quantum mechanisms.

Implications for Security and Applications

This treatment of randomness has significant implications for security-related applications such as cryptography, where the unpredictability of random numbers is paramount. By providing a method to rigorously measure and enhance the quality of randomness against side information, the research offers a pathway to more secure RNGs that are less vulnerable to exploitation.

Future Directions

The paper opens several avenues for further research, notably improving QRNG designs to minimize noise and enhancing post-processing algorithms to maximize true randomness extraction. This research can encourage the development of more standardized metrics and protocols for future QRNGs across different industries.

In sum, this paper addresses a critical need in randomness certification, offering both theoretical insights and practical tools to improve the reliability of QRNGs. The proposed framework not only furnishes a robust method to verify true randomness in quantum systems but also prompts further exploration in quantum communication and computation where randomness plays a crucial role.