Self-testing multipartite entangled states through projections onto two systems
- Creators
- Šupić, I.
- Coladangelo, A.
- Augusiak, R.
- Acín, A.
Abstract
Finding ways to test the behaviour of quantum devices is a timely enterprise, especially in light of the rapid development of quantum technologies. Device-independent self-testing is one desirable approach, as it makes minimal assumptions on the devices being tested. In this work, we address the question of which states can be self-tested. This has been answered recently in the bipartite case (Coladangelo et al 2017 Nat. Commun. 8 15485), while it is largely unexplored in the multipartite case, with only a few scattered results, using a variety of different methods: maximal violation of a Bell inequality, numerical SWAP method, stabiliser self-testing etc. In this work, we investigate a simple, and potentially unifying, approach: combining projections onto two-qubit spaces (projecting parties or degrees of freedom) and then using maximal violation of the tilted CHSH inequalities. This allows one to obtain self-testing of Dicke states and partially entangled GHZ states with two measurements per party, and also to recover self-testing of graph states (previously known only through stabiliser methods). Finally, we give the first self-test of a class of multipartite qudit states: we generalise the self-testing of partially entangled GHZ states by adapting techniques from (Coladangelo et al 2017 Nat. Commun. 8 15485), and show that all multipartite states which admit a Schmidt decomposition can be self-tested with few measurements.
Additional Information
© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 9 April 2018; Accepted 7 August 2018; Accepted Manuscript online 7 August 2018; Published 28 August 2018. The authors thank Flavio Baccari, Marc Roda, Alexia Salavrakos and Thomas Vidick for useful discussions. This work was supported by Spanish MINECO (QIBEQI FIS2016-80773-P and Severo Ochoa SEV-2015-0522), the AXA Chair in Quantum Information Science, Generalitat de Catalunya (CERCA Programme), Fundació Privada Cellex and ERC CoG QITBOX. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 705109. IŠ acknowledges the support of 'Obra Social La Caixa 2016' and COST project CA16218, NANOCOHYBRI. AC is supported by AFOSR YIP award number FA9550-16-1-0495. RA acknowledges the support from the Foundation for Polish Science through the First Team project No First TEAM/2017-4/31 co-financed by the European Union under the European Regional Development Fund.Attached Files
Published - Šupić_2018_New_J._Phys._20_083041.pdf
Submitted - 1707.06534.pdf
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Additional details
- Eprint ID
- 89601
- Resolver ID
- CaltechAUTHORS:20180913-072418859
- QIBEQI FIS2016-80773-P
- Ministerio de Economía, Industria y Competitividad (MINECO)
- SEV-2015-0522
- Ministerio de Economía, Industria y Competitividad (MINECO)
- AXA Research Fund
- Generalitat de Catalunya
- Fundació Privada Cellex
- CoG QITBOX
- European Research Council (ERC)
- 705109
- Marie Curie Fellowship
- Obra Social La Caixa 2016
- CA16218
- European Cooperation in Science and Technology (COST)
- FA9550-16-1-0495
- Air Force Office of Scientific Research (AFOSR)
- TEAM/2017-4/31
- Fundacja na rzecz Nauki Polskiej
- European Regional Development Fund
- Created
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2018-09-13Created from EPrint's datestamp field
- Updated
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2022-07-12Created from EPrint's last_modified field