Quantum violations in the Instrumental scenario and their relations to the Bell scenario

Thomas Van Himbeeck , Jonatan Bohr Brask , Stefano Pironio , Ravishankar Ramanathan , Ana Belen Sainz , Elie Wolfe

Abstract

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.
Author Thomas Van Himbeeck
Thomas Van Himbeeck,,
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, Jonatan Bohr Brask
Jonatan Bohr Brask,,
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, Stefano Pironio
Stefano Pironio,,
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, Ravishankar Ramanathan
Ravishankar Ramanathan,,
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, Ana Belen Sainz (ICTQT)
Ana Belen Sainz,,
- International Centre for Theory of Quantum Technologies
, Elie Wolfe
Elie Wolfe,,
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Journal seriesQuantum, ISSN 2521-327X, (N/A 140 pkt)
Issue year2019
Vol3
Pages1-12
Publication size in sheets0.55
Article number186
DOIDOI:10.22331/q-2019-09-16-186
URL https://doi.org/10.22331/q-2019-09-16-186
Languageen angielski
LicenseJournal (articles only); published final; Uznanie Autorstwa (CC-BY); with publication
Score (nominal)140
Score sourcejournalList
ScoreMinisterial score = 140.0, 28-01-2020, ArticleFromJournal
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