Abstract

In this paper we design a protocol to extract random bits with an arbitrarily low bias from a single arbitrarily weak min-entropy block source in a device independent setting. The protocol employs Mermin devices that exhibit super-classical correlations. Number of devices used scales polynomially in the length of the block n, containing entropy of at least two bits. Our protocol is robust, it can tolerate devices that malfunction with a probability dropping polynomially in n at the cost of constant increase of the number of devices used.

Highlights

  • High quality randomness is a very useful resource in many computation and cryptographic tasks

  • Even though we cannot fully predict certain processes it is very difficult to argue that they produce perfect randomness – independent and unbiased bits

  • The problem of imperfect randomness has a long history in classical computer science and long line of research was devoted to randomness extraction – algorithms to transform imperfect sources of randomness into perfect ones [3]

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Summary

Introduction

High quality randomness is a very useful resource in many computation and cryptographic tasks. Device-independent Randomness Extraction for Arbitrarily Weak Min-entropy Source deterministic. Thanks to Bell-type experiments, it is possible to certify by classical procedures that quantum processes are being observed and intrinsic randomness is being produced. This is the basic idea behind device independent randomness extraction. One can view device-independent randomness extraction as quantum protocol for extracting randomness from a single weak source – a task that is classically impossible. Each new block has high min-entropy, even conditioned on the previous ones and any information of the adversary This is a generalization of Santha-Vazirani sources [5], which can be viewed as block sources with n = 1. The main difference between the two results is that we work with min-entropy block sources, while their results hold for general min-entropy sources

Device Independent Concept and Mermin Inequality
Single-round protocol
Multiple-round protocol
Robustness
Findings
Conclusion

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