Search
Abstract
Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations of a few inequalities at once. Here we systematically study monogamy relations between correlation Bell inequalities both within quantum theory and under the sole assumption of no signalling. We first investigate the trade-offs in Bell violations arising from the uncertainty relation for complementary binary observables, and exhibit several network configurations in which a tight trade-off arises in this fashion. We then derive a tight trade-off relation which cannot be obtained from the uncertainty relation showing that it does not capture monogamy entirely. The results are extended to Bell inequalities involving different number of parties and find applications in device-independent secret sharing and device-independent randomness extraction. Although two multipartite Bell inequalities may be violated simultaneously, we show that genuine multi-party non-locality, as evidenced by a generalised Svetlichny inequality, does exhibit monogamy property. Finally, using the relations derived we reveal the existence of flat regions in the set of quantum correlations.
Citations
-
9
CrossRef
-
0
Web of Science
-
7
Scopus
Authors (2)
-
Ravishankar Ramanathan
Cite as
Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1103/PhysRevA.98.022133
- License
- Copyright (2018 American Physical Society)
Keywords
Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
PHYSICAL REVIEW A
no. 98,
edition 2,
pages 1 - 15,
ISSN: 2469-9926 - Language:
- English
- Publication year:
- 2018
- Bibliographic description:
- Ramanathan R., Mironowicz P.: Trade-offs in multiparty Bell-inequality violations in qubit networks// PHYSICAL REVIEW A. -Vol. 98, iss. 2 (2018), s.1-15
- DOI:
- Digital Object Identifier (open in new tab) 10.1103/physreva.98.022133
- Verified by:
- Gdańsk University of Technology
seen 145 times
Recommended for you
Elemental and tight monogamy relations in nonsignaling theories
- R. Augusiak,
- M. Demianowicz,
- M. Pawłowski
- + 2 authors
Bound on Bell inequalities by fraction of determinism and reverse triangle inequality
- P. Joshi,
- K. Horodecki,
- M. Horodecki
- + 5 authors
Relationship between semi- and fully-device-independent protocols
- H. Li,
- P. A. Mironowicz,
- M. Pawłowski
- + 7 authors