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

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


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.

► BibTeX data

► References

[1] Acínand Masanes ``Certified randomness in quantum physics'' Nature 540, 213-219 (2016).

[2] Brunner, Cavalcanti, Pironio, Scarani, and Wehner, ``Bell nonlocality'' Rev. Mod. Phys. 86, 419-478 (2014).

[3] Pironio, Acín, Massar, Boyer de la Giroday, Matsukevich, Maunz, Olmschenk, Hayes, Luo, Manning, and Monroe, ``Random numbers certified by Bell'' Nature 464, 1021 (2010).

[4] Vaziraniand Vidick ``Certifiable quantum dice'' Phil. Trans. R. Soc. A 370, 3432-3448 (2012).

[5] Coudronand Yuen ``Infinite randomness expansion and amplification with a constant number of devices'' (2013).

[6] Millerand Shi ``Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices'' J. ACM 63, 33:1-33:63 (2016).

[7] Chung, Shi, and Wu, ``Physical randomness extractors: generating random numbers with minimal assumptions'' (2014).

[8] Bennett, Bernstein, Popescu, and Schumacher, ``Concentrating partial entanglement by local operations'' Phys. Rev. A 53, 2046-2052 (1996).

[9] Acín, Massar, and Pironio, ``Randomness versus Nonlocality and Entanglement'' Phys. Rev. Lett. 108, 100402 (2012).

[10] Werner ``Quantum states with Einstein'' Phys. Rev. A 40, 4277-4281 (1989).

[11] Curchod, Johansson, Augusiak, Hoban, Wittek, and Acín, ``Unbounded randomness certification using sequences of measurements'' Phys. Rev. A 95, 020102 (2017).

[12] Dupuis, Fawzi, and Renner, ``Entropy accumulation'' (2016).

[13] Arnon-Friedman, Renner, and Vidick, ``Simple and tight device-independent security proofs'' (2016).

[14] Arnon-Friedman, Dupuis, Fawzi, Renner, and Vidick, ``Practical device-independent quantum cryptography via entropy accumulation'' Nat. Commun. 9, 459 (2018).

[15] Bampsand Pironio ``Sum-of-squares decompositions for a family of Clauser'' Phys. Rev. A 91, 052111 (2015).

[16] Hoeffding ``Probability Inequalities for Sums of Bounded Random Variables'' J. Am. Stat. Assoc. 58, 13-30 (1963).

[17] Reichardt, Unger, and Vazirani, ``A classical leash for a quantum system: command of quantum systems via rigidity of CHSH'' (2012).

[18] Wilde ``Quantum Information Theory'' Cambridge University Press (2013).

[19] Nielsenand Chuang ``Quantum Computation and Quantum Information'' Cambridge University Press (2000).

[20] Cleveand DiVincenzo ``Schumacher's quantum data compression as a quantum computation'' Phys. Rev. A 54, 2636-2650 (1996).

[21] König, Renner, and Schaffner, ``The operational meaning of min- and max-entropy'' IEEE Trans. Inf. Theory 55, 4337-4347 (2009).

[22] Tomamichel ``A framework for non-asymptotic quantum information theory'' thesis (2012).

[23] Schumacher ``Quantum coding'' Phys. Rev. A 51, 2738-2747 (1995).

[24] Coverand Thomas ``Elements of Information Theory'' John Wiley & Sons (2012).

[25] Winter ``Coding theorem and strong converse for quantum channels'' IEEE 45, 2481-2485 (1999).

[26] Ogawaand Nagaoka ``A new proof of the channel coding theorem via hypothesis testing in quantum information theory'' 2002 IEEE 73 (2002).

Cited by

[1] 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).

[2] 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).

[3] Rotem Arnon-Friedman, "Reductions to IID in Device-independent Quantum Information Processing", arXiv:1812.10922.

The above citations are from Crossref's cited-by service (last updated successfully 2020-04-06 22:29:54) and SAO/NASA ADS (last updated successfully 2020-04-06 22:29:55). The list may be incomplete as not all publishers provide suitable and complete citation data.