CGLMP and Bell–CHSH formulations of non-locality: a comparative study

Abstract

The CGLMP prescription of non-locality is known to identify certain states that satisfy the Bell–CHSH inequality to be non-local. The demonstration is, however, restricted to a specific family of states. In this paper, we address the converse question: can there be states that satisfy the CGLMP inequality but violate Bell–CHSH? We find the answer to be in the affirmative. Examining coupled \(4 \times 4\) level systems, we find that there exist a large number of such states. As a direct consequence, states that violate the CGLMP inequality do not form a superset over the ones that violate Bell–CHSH.

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Acknowledgements

Radha thanks the Department of Science and Technology (DST), India, for funding her research under the WOS-A Women’s Scientist Scheme. Soumik thanks Council of Scientific and Industrial Research (CSIR), India, for funding his research. The authors would also like to thank the referees for their valuable comments and suggestions.

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Correspondence to Radha Pyari Sandhir.

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Sandhir, R.P., Adhikary, S. & Ravishankar, V. CGLMP and Bell–CHSH formulations of non-locality: a comparative study. Quantum Inf Process 16, 263 (2017). https://doi.org/10.1007/s11128-017-1712-x

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Keywords

  • Bell inequality
  • Non-locality
  • Higher-dimensional systems