Device-independent randomness amplification with a single device

Abstract

Expansion and amplification of weak randomness with untrusted quantum devices has recently become a very fruitful topic of research. Here we contribute with a procedure for amplifying a single weak random source using tri-partite GHZ-type entangled states. If the quality of the source reaches a fixed threshold $R=\frac{1}{4}\log_{2}(10)$, perfect random bits can be produced. This technique can be used to extract randomness from sources that can't be extracted neither classically, nor by existing procedures developed for Santha-Vazirani sources. Our protocol works with a single fault-free device decomposable into three non-communicating parts, that is repeatedly reused throughout the amplification process.Comment: 23 pages, 4 figures, accepted in PL

Quantum Random Number Generation for 1.25-GHz Quantum Key Distribution Systems

“…To get a bound on the min-entropy of the source, we consider a Santha-Vazirani type of weak source of randomness [20,21], which generates a sequence of weak random bits where the probability distribution of each bit, conditioned on the previously generated bits, is bounded by some fixed real parameter 0 < δ ≤ 1/2. In particular, let the X 1 , X 2 , .…”

Quantum random number generators

“…( 39), (Gallego et al, 2013) give a quantum randomness amplification protocol that is valid for arbitrarily weak sources of entropy. Further protocols can take any input weak source with a bounded nonzero min-entropy (Bouda et al, 2014;Chung et al, 2014;Plesch and Pivoluska, 2014) and give practical ways to use Santha-Vazirani sources, requiring only a limited number of independent devices (Brandão et al, 2016).…”

Semi-device-independent random number generation with flexible assumptions

“…This assumption requires us to solve an optimization problem of the form as in Eq. (13), where now the condition f(γ) = c γ reads X 1 i¼0 iγ i ¼ μ; (16) and p i = 1 − π i . In the section "Mean photon number analysis" we show that the solution to this optimization problem contains only three non-zero probabilities γ i :…”

“…11 and developed in refs. [12][13][14][15][16][17][18][19][20][21] , are called device independent (DI-RNGs), because they assume very little about the hardware they use. The security proof for these devices is usually based on Bell-type arguments: the RNG is composed of several non-communicating parts and runs a set of randomness-generation rounds, which involve a predetermined quantum measurement.…”