Device-independent randomness generation with sublinear shared quantum resources

Cédric Bamps, Serge Massar, and Stefano Pironio

Laboratoire d'Information Quantique, CP 224, Université libre de Bruxelles (ULB), 1050 Brussels, Belgium

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Abstract

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.

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[1] Elie Wolfe, David Schmid, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens, "Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes", Quantum 4, 280 (2020).

[2] Ivan Šupić and Joseph Bowles, "Self-testing of quantum systems: a review", Quantum 4, 337 (2020).

[3] 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", Quantum 3, 186 (2019).

[4] Peter J. Brown, Sammy Ragy, and Roger Colbeck, "A Framework for Quantum-Secure Device-Independent Randomness Expansion", IEEE Transactions on Information Theory 66 5, 2964 (2020).

[5] Rotem Arnon-Friedman, Renato Renner, and Thomas Vidick, "Simple and Tight Device-Independent Security Proofs", arXiv:1607.01797, SIAM Journal on Computing 48 1, 181 (2019).

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The above citations are from Crossref's cited-by service (last updated successfully 2020-10-28 08:25:53) and SAO/NASA ADS (last updated successfully 2020-10-28 08:25:54). The list may be incomplete as not all publishers provide suitable and complete citation data.