The Effect of the Number of Entangled Photons on the Number of Coincidences Rate, Bell’s Inequality and the Error Rate by the Delphi Program

SIB. Mustafa

Institute of Laser, Sudan University of Science and Technology, Khartoum, Sudan.

Nafie A. Almuslet

Chief of Advisory Board / Aalborg Academy of Science and Technology, Turkey.

Zienb K. Osman

Department of Physics, Sudan University of Science and Technology, Khartoum, Sudan.

Tarig H. Abdeelh

Defence Industrial System, Khartoum, Sudan.

KH. M. Haroun *

Faculty of Education, ALzaiem Alazhari University, Khartoum, Sudan.

*Author to whom correspondence should be addressed.


Quantum cryptography is a science that relies on the use of a protocol designed to exploit quantum mechanical phenomena to achieve the secrecy of cryptographic keys. This work aimed to generate a quantum key based on polarization-entangled photon pairs; to eliminate the error by implementing the BB89 protocol using the Delphi language program in order to obtain a high degree of security. The results explain the effect of the number of EPR photons pair running from (500-10000) photons on the number of coincidences, expected error and Bell's parameter discussed as; Total coincidences of the Bell – CHSH increases with increasing of EPR pairs, and values were stable when EPR pairs were increased, there was a small random change in the expected error rate (in case of no eavesdropping).This study concludes thatTotal coincidences of the Bell and expected error are affected by the number of entangled photons.The increasing of the length of key must increase the number of EPR and decrease the Error and Bell's value must be stable.

Keywords: Quantum Key Distribution (QKD), Einstein- Podolesky- Rosen (EPR)

How to Cite

Mustafa, S., Almuslet, N. A., Osman, Z. K., Abdeelh, T. H., & Haroun, K. M. (2022). The Effect of the Number of Entangled Photons on the Number of Coincidences Rate, Bell’s Inequality and the Error Rate by the Delphi Program. Physical Science International Journal, 26(8), 55–64.


Download data is not yet available.


Einstein A, B. Podolsky, N. Rosen. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete: Physical Review. 1935;47(10):777-780.

J. S. Bell. On the Einstein Podolosky Rosen Paradox. Physics. 1964;1:195- 200.

Fritz W. Bopp. Causal classical physics in time symmetric quantum mechanics. 4th International Electronic Conference on Entropy and Its Applications, Basel, Switzerland; 2017. Available:

Nicolas Gisin, GrégoireRibordy, Wolfgang Tittel, Hugo Zbinden. Quantum cryptography: Rev. Mod. Phys. 2002;74:145.

F. Flamini, N. Spagnolo, F. Sciarrino. Photonic quantum information processing: A review. Rep. Prog. Phys. 2018;82.016001.

Minal Lopes and NishaSarwade. Cryptography from Quantum Mechanical Viewpoint: International Journal on Cryptography and Information Security (IJCIS). 2014;4(2).

Nurhaci AI, Syambas NR. Quantum Key Distribution (QKD) Protocols: A Survey," 2018 4th International Conference on Wireless and Telematics (ICWT); 2018.

Gerardo Iovane. Computational quantum key distribution (CQKD) on decentralized ledger and blockchain. Journal of Discrete Mathematical Sciences and Cryptography. 2021;24:4.1021-1042.

Abudhahir Buhari, Zuriati Ahmad Zukarnain, Subramaniam SK, Hishamuddin Zainuddin, Suhairi Saharudin. An efficient modeling and simulation of quantum key distribution protocols using Opti System: IEEE Symposium on Industrial Electronics and Applications. 2012;84-89.

Kalra M, Poonia RC. Design a new protocol and compare with BB84 protocol for quantum key distribution. In: Bansal, J., Das, K., Nagar, A., Deep, K., Ojha, A. (eds) Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing: Springer. Singapore. 2019; 817:978-981.

Weier H. Experimental quantum cryptography. Diploma Dissertation, Technical University of Munich; 2003 Dec.

Bennett CH. Quantum cryptography using any two nonorthogonal states: Physical review letters. 1992 May 25;68(21):3121.

Ekert AK. Quantum cryptography based on Bell’s theorem: Phys. Rev. 1991;67:661–663.

Ma X, Fung CHF, Lo HK. Quantum key distribution with entangled photon sources: Phys. Rev. 2007;76:012307.

Acín, Brunner N, Gisin N, Massar S, Pironio S, Scarani V. Device-independent security of quantum cryptography against collective attacks: Phys. Rev. 2007;98:230501.

Maki AM. Simulation of quantum key distribution based on entangled pairs of photons using the basic ekert protocol. M.Sc. Thesis University of Baghdad; 2004.

Mathieu Guillermin, Tom Dedeurwaerdere. Epistemic values, bell's inequalities and realism: The case of contemporary approaches to quantum mechanics. SSRN .2013;10(2139):2284104

Scully MO, Zubairy MS. Quantum Optics, Combridge University Press. UK; 1997.

Rau M, Heindel T, Unsleber S, Braun T, Fischer J, Frick S, Nauerth S, Schneider C, Vest G, Reitzenstein S, Kamp M, Forchel A, Höfling S, Weinfurter H. Free space quantum key distribution over 500 meters using electrically driven quantum dot single-photon sources—A proof of principle experiment. New J. Phys. 2014;16: 043003.

Zeilinger (Eds). The physics of quantum information. Springer Inc.; 1998. ISBN-13: 978-3540667780

Naik S, Peterson CG, White AG, Bergland AJ, Kwiat PG. Entangled state quantum cryptography: eavesdropping on the ekert protocol. Physical Review Letters. 1999;84.20:4733-4736

Faraj ST. Quantum cryptography key distribution in optical communication networks. PhD Thesis Submitted to the Collage of Engineering of The Former Sadam University, Electronic and Communication Engineering; 1999.

Vladimir K. Ignatovich. Closer look at EPR paradox and bell’s inequality: American Journal of Modern Physics and Application. 2015;2(2):16-20.

Mafu M. A simple security proof for entanglement-based quantum key distribution: Journal of Quantum Information Science. 2016;6:296-303. DOI: 10.4236/jqis.2016.64018.

Hitesh Singh, Gupta DL, Singh AK. Quantum Key Distribution Protocols: A Review: IOSR Journal of Computer Engineering (IOSR). 2014;16(2):1-9.

Basset et al. Quantum Sci. Technol. 2023;8:025002.