Bounding sets of sequential quantum correlations and device-independent randomness certification

Joseph Bowles; Flavio Baccari; Alexia Salavrakos

doi:10.22331/q-2020-10-19-344

Bounding sets of sequential quantum correlations and device-independent randomness certification

Joseph Bowles¹, Flavio Baccari^1,2, and Alexia Salavrakos¹

¹ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
²Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany

Published:	2020-10-19, volume 4, page 344
Eprint:	arXiv:1911.11056v4
Doi:	https://doi.org/10.22331/q-2020-10-19-344
Citation:	Quantum 4, 344 (2020).

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Abstract

An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the NPA hierarchy; an infinite sequence of semidefinite programs that provides increasingly tighter outer approximations to the desired set of correlations. In this work we consider a more general scenario in which one performs sequences of local measurements on an entangled state of arbitrary dimension. We show that a simple adaptation of the original NPA hierarchy provides an analogous hierarchy for this scenario, with comparable resource requirements and convergence properties. We then use the method to tackle some problems in device-independent quantum information. First, we show how one can robustly certify over 2.3 bits of device-independent local randomness from a two-quibt state using a sequence of measurements, going beyond the theoretical maximum of two bits that can be achieved with non-sequential measurements. Finally, we show tight upper bounds to two previously defined tasks in sequential Bell test scenarios.

► BibTeX data

@article{Bowles2020boundingsetsof,
  doi = {10.22331/q-2020-10-19-344},
  url = {https://doi.org/10.22331/q-2020-10-19-344},
  title = {Bounding sets of sequential quantum correlations and device-independent randomness certification},
  author = {Bowles, Joseph and Baccari, Flavio and Salavrakos, Alexia},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {344},
  month = oct,
  year = {2020}
}

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Bounding sets of sequential quantum correlations and device-independent randomness certification

Abstract

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