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Violation of space–time Bell-CHSH inequality beyond the Tsirelson bound and quantum cryptography

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Abstract

Here we show that if we insert context-dependent local unitary evolutions into the spatial (i.e. normal) Bell–Clauser–Horne–Shimony–Holt (Bell-CHSH) test, then it is possible to violate the space–time Bell-CHSH inequality maximally (i.e. up to 4). The correct context dependency can be achieved via post-selection. However, this does not contradict the Tsirelson quantum bound (\(2\sqrt{2}\)), because the latter has been derived without taking into consideration the context-dependent unitary evolutions and / or post-selection. As an important application, this leads to a more efficient (in terms of resource (singlets) and classical communication) and more sensitive (to eavesdropping) quantum key distribution (QKD) protocol, compared to Ekert’s and Wigner’s QKD protocols.

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Acknowledgements

The author acknowledges the useful discussions with Prof. T S Mahesh, Prof. R Srikanth, S Aravinda, Deepak Khurana, V S Anjusha and Soham Pal. Finally, he would like to thank anonymous referees for suggesting to quantify the amount of CC involved in various QKD protocols and for pointing out the fact that violation beyond Tsirelson bound is not due to any kind of possible loop holes in performing the Bell test.

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  1. NMR Research Centre and Department of Physics, Indian Institute of Science Education and Research, Pune, 411 008, India

    C S Sudheer Kumar

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Correspondence to C S Sudheer Kumar.

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Sudheer Kumar, C.S. Violation of space–time Bell-CHSH inequality beyond the Tsirelson bound and quantum cryptography. Pramana - J Phys 93, 67 (2019). https://doi.org/10.1007/s12043-019-1830-3

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