Journal
NEW JOURNAL OF PHYSICS
Volume 23, Issue 4, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1367-2630/abf2fb
Keywords
quantum correlations; monogamy relations; information-theoretical distance; triangle inequality
Categories
Funding
- Singapore Ministry of Education Academic Research Fund [MOE2012-T3-1-009]
- Research Centres of Excellence programme by the National Research Foundation (NRF) Singapore
- Ministry of Education, Singapore
- National Research Foundation of Korea (NRF) - Korea Government (MSIT) [2019R1A2C2005504, 2019M3E4A1079666, NRF-2020M3E4A1079792]
- National Research Foundation of Korea [2019R1A2C2005504] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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In this study, genuine monogamy relations for a class of Bell type inequalities are proposed using simple geometric properties of probabilistic spaces and the no-signaling principle, extending the method to qubits and d-dimensional tripartite systems and demonstrating their monogamous nature.
Quantum correlations are subject to certain distribution rules represented by so-called monogamy relations. Derivation of monogamy relations for multipartite systems is a non-trivial problem, as the multipartite correlations reveal their behaviors in a way different from bipartite systems. We here show that simple geometric properties of probabilistic spaces, in conjunction with no-signaling principle, lead to genuine monogamy relations for a large class of Bell type inequalities for many qubits. The term of 'genuine' implies that only one out of N Bell inequalities exhibits a quantum violation. We also generalize our method to qudits. Using the similar geometric approach with a quasi-distance employed, we derive Svetlichny-Zohren-Gill type Bell inequalities for d-dimensional tripartite systems, and show their monogamous nature.
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