Maximal Randomness Generation from Steering Inequality Violations Using Qudits

Physical Review Letters
Paul Skrzypczyk, Daniel Cavalcanti

Abstract

We consider the generation of randomness based upon the observed violation of an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided device-independent randomness generation. We show that in the simplest scenario-involving only two parties and two measurements for the uncharacterised party with d outcomes-that there exist EPR steering inequalities whose maximal violation certifies maximal randomness generation, equal to log(d) bits. We further show that all pure partially entangled full-Schmidt-rank states in all dimensions can achieve maximal violation of these inequalities, and thus lead to maximal randomness generation in the one-sided device-independent setting. More generally, the amount of randomness that can be generated is given by a semidefinite program, which we use to study the behavior for nonmaximal violations of the inequalities.

References

Jan 22, 2002·Physical Review Letters·Daniel CollinsSandu Popescu
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Jun 20, 2012·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Umesh Vazirani, Thomas Vidick
Dec 9, 2016·Nature·Antonio Acín, Lluis Masanes
Dec 23, 2016·Reports on Progress in Physics·D Cavalcanti, P Skrzypczyk
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Jan 18, 2018·Physical Review Letters·Alexia SalavrakosStefano Pironio
Mar 10, 2018·Science·Jianwei WangMark G Thompson

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Citations

May 9, 2021·Nature Communications·Xiaojiong ChenJianwei Wang
Jun 11, 2021·Physical Review Letters·Sébastien DesignolleNicolas Brunner

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