In quantum cryptography, device-independent (DI) protocols can be certified secure without requiring assumptions about the inner workings of the devices used to perform the protocol. In order to display nonlocality, which is an essential feature in DI protocols, the device must consist of at least two separate components sharing entanglement. This raises a fundamental question: how much entanglement is needed to run such DI protocols? We present a two-device protocol for DI random number generation (DIRNG) which produces approximately $n$ bits of randomness starting from $n$ pairs of arbitrarily weakly entangled qubits. We also consider a variant of the protocol where $m$ singlet states are diluted into $n$ partially entangled states before performing the first protocol, and show that the number $m$ of singlet states need only scale sublinearly with the number $n$ of random bits produced. Operationally, this leads to a DIRNG protocol between distant laboratories that requires only a sublinear amount of quantum communication to prepare the devices.
 Pironio, Acín, Massar, Boyer de la Giroday, Matsukevich, Maunz, Olmschenk, Hayes, Luo, Manning, and Monroe, ``Random numbers certified by Bell'' Nature 464, 1021 (2010).
 Curchod, Johansson, Augusiak, Hoban, Wittek, and Acín, ``Unbounded randomness certification using sequences of measurements'' Phys. Rev. A 95, 020102 (2017).
 Arnon-Friedman, Dupuis, Fawzi, Renner, and Vidick, ``Practical device-independent quantum cryptography via entropy accumulation'' Nat. Commun. 9, 459 (2018).
 Wilde ``Quantum Information Theory'' Cambridge University Press (2013).
 Nielsenand Chuang ``Quantum Computation and Quantum Information'' Cambridge University Press (2000).
 Coverand Thomas ``Elements of Information Theory'' John Wiley & Sons (2012).
 Thomas Van Himbeeck, Jonatan Bohr Brask, Stefano Pironio, Ravishankar Ramanathan, Ana Belén Sainz, and Elie Wolfe, "Quantum violations in the Instrumental scenario and their relations to the Bell scenario", arXiv:1804.04119 (2018).
 Rotem Arnon-Friedman, "Reductions to IID in Device-independent Quantum Information Processing", arXiv:1812.10922 (2018).
The above citations are from SAO/NASA ADS (last updated 2019-01-22 23:32:56). The list may be incomplete as not all publishers provide suitable and complete citation data.
On Crossref's cited-by service no data on citing works was found (last attempt 2019-01-22 23:32:54).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.