A Quantum Random Number Generator Certified by Value Indefiniteness

In this paper we propose a quantum random number generator (QRNG) which utilizes an entangled photon pair in a Bell singlet state, and is certified explicitly by value indefiniteness. While "true randomness" is a mathematical impossibility, the certification by value indefiniteness ensures the quantum random bits are incomputable in the strongest sense. This is the first QRNG setup in which a physical principle (Kochen-Specker value indefiniteness) guarantees that no single quantum bit produced can be classically computed (reproduced and validated), the mathematical form of bitwise physical unpredictability. The effects of various experimental imperfections are discussed in detail, particularly those related to detector efficiencies, context alignment and temporal correlations between bits. The analysis is to a large extent relevant for the construction of any QRNG based on beam-splitters. By measuring the two entangled photons in maximally misaligned contexts and utilizing the fact that two rather than one bitstring are obtained, more efficient and robust unbiasing techniques can be applied. A robust and efficient procedure based on XORing the bitstrings together---essentially using one as a one-time-pad for the other---is proposed to extract random bits in the presence of experimental imperfections, as well as a more efficient modification of the von Neumann procedure for the same task. Some open problems are also discussed.Comment: 25 pages, 3 figure

Privacy Amplification in the Isolated Qubits Model

Isolated qubits are a special class of quantum devices, which can be used to implement tamper-resistant cryptographic hardware such as one-time memories (OTM's). Unfortunately, these OTM constructions leak some information, and standard methods for privacy amplification cannot be applied here, because the adversary has advance knowledge of the hash function that the honest parties will use. In this paper we show a stronger form of privacy amplification that solves this problem, using a fixed hash function that is secure against all possible adversaries in the isolated qubits model. This allows us to construct single-bit OTM's which only leak an exponentially small amount of information. We then study a natural generalization of the isolated qubits model, where the adversary is allowed to perform a polynomially-bounded number of entangling gates, in addition to unbounded local operations and classical communication (LOCC). We show that our technique for privacy amplification is also secure in this setting.Comment: v2: 24 pages, stronger security definition, better proof technique, improved presentatio

Deterministic extraction from weak random sources

In this research monograph, the author constructs deterministic extractors for several types of sources, using a methodology of recycling randomness which enables increasing the output length of deterministic extractors to near optimal length