Quantum Entanglement and Its Classification Protocols

Authors

  • Amirul Asyraf Zhahir Faculty of Science and Technology, Universiti Sains Islam Malaysia, 71800 Nilai, Negeri Sembilan, Malaysia. https://orcid.org/0000-0001-7014-1704
  • Siti Munirah Mohd Kolej PERMATA Insan, Universiti Sains Islam Malaysia, 71800 Nilai, Negeri Sembilan, Malaysia. https://orcid.org/0000-0002-0153-6435
  • Mohd Sham Mohamad Centre for Mathematical Sciences, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia.
  • Mohd Ilias M Shuhud Faculty of Science and Technology, Universiti Sains Islam Malaysia, 71800 Nilai, Negeri Sembilan, Malaysia. https://orcid.org/0000-0001-7731-0793
  • Bahari Idrus Center for Artificial Intelligence Technology (CAIT), Faculty of Information Science and Technology Bangi, Selangor, Malaysia.
  • Hishamuddin Zainuddin XIAMEN UNIVERSITY MALAYSIA
  • Nurhidaya Mohamad Jan Department of Physics, School of Mathematics and Physics, Xiamen University Malaysia, 43900 Sepang, Selangor, Malaysia.

DOI:

https://doi.org/10.33102/mjosht.v10i2.408

Keywords:

Quantum entanglement, Entanglement classification, LU, LOCC, SLOCC

Abstract

Quantum entanglement has its own major role in quantum information theory. Its application in numerous areas namely quantum computing, quantum cryptography and quantum teleportation are proven vital and essential. Over the last decades, the interests in quantum entanglement have grown and significant progress in quantum computing has been revealed. However, the classification of entanglement was proved to be challenging especially in a higher qubit-dimensional system setting. In this review, indexed literature as the secondary resource was chosen by specific keywords from several database. In reference to the literatures review, there exists several entanglement classifications protocols that will be presented in this paper namely local unitary (LU), local operations and classical communication (LOCC), and stochastic local operations and classical communication (SLOCC). This study will offer a better understanding of quantum entanglement and the entanglement classification protocols. 

Downloads

Download data is not yet available.

References

Zhahir, A.A., S.M. Mohd, M.I.M. Shuhud, B. Idrus, H. Zainuddin, N.M. Jan, and M.R. Wahiddin, "Quantum Computing and Its Application", International Journal of Advanced Research in Technology and Innovation Vol. 4, No. 1, pp. 55-65, 2022.

Qian, K., K. Wang, L. Chen, Z. Hou, M. Krenn, S. Zhu, and X.-s. Ma, "Multiphoton non-local quantum interference controlled by an undetected photon", Nature Communications Vol. 14, No. 1, pp. 1480, 2023.

Shen, S., C. Yuan, Z. Zhang, H. Yu, R. Zhang, C. Yang, H. Li, Z. Wang, Y. Wang, G. Deng, H. Song, L. You, Y. Fan, G. Guo, and Q. Zhou, "Hertz-rate metropolitan quantum teleportation", Light: Science & Applications Vol. 12, No. 1, 2023.

Fakhruldeen, H.F., R.A. Alkaabi, I. Jabbar, I. Al-Kharsan, and S. Shoja, "Post-quantum Techniques in Wireless Network Security: An Overview", Malaysian Journal of Fundamental and Applied Sciences Vol. 19, No., pp. 337-344, 2023.

Dong, M., M. Zimmermann, D. Heim, H. Choi, G. Clark, A.J. Leenheer, K.J. Palm, A. Witte, D. Dominguez, G. Gilbert, M. Eichenfield, and D. Englund, "Programmable photonic integrated meshes for modular generation of optical entanglement links", npj Quantum Information Vol. 9, No. 1, pp. 42, 2023.

Ren, S.-Y., W.-Q. Wang, Y.-J. Cheng, L. Huang, B.-Z. Du, W. Zhao, G.-C. Guo, L.-T. Feng, W.-F. Zhang, and X.-F. Ren, "Photonic-chip-based dense entanglement distribution", PhotoniX Vol. 4, No. 1, pp. 12, 2023.

Mooney, G.J., C.D. Hill, and L.C.L. Hollenberg, "Entanglement in a 20-Qubit Superconducting Quantum Computer", Scientific Reports Vol. 9, No. 1, pp. 13465, 2019.

Letzter, R. [Online]. Available: https://www.scientificamerican.com/article/chinese-researchers-achieve-stunning-quantum-entanglement-record/#

Asif, N., U. Khalid, A. Khan, T.Q. Duong, and H. Shin, "Entanglement detection with artificial neural networks", Scientific Reports Vol. 13, No. 1, pp. 1562, 2023.

Wang, Y., Y. Li, Z.-Q. Yin, and B. Zeng, "16-qubit IBM universal quantum computer can be fully entangled", npj Quantum Information Vol. 4, No., pp. 1-6, 2018.

Sabín, C., "Digital quantum simulation of quantum gravitational entanglement with IBM quantum computers", EPJ Quantum Technology Vol. 10, No. 1, pp. 4, 2023.

Ball, P., "First quantum computer to pack 100 qubits enters crowded race", Vol. 599, No., pp. 542, 2021.

IBM. [Online]. Available: https://newsroom.ibm.com/2022-11-09-IBM-Unveils-400-Qubit-Plus-Quantum-Processor-and-Next-Generation-IBM-Quantum-System-Two

Gambetta, J. [Online]. Available: https://www.ibm.com/quantum/blog/quantum-roadmap-2033

Zeitgeist, Q. [Online]. Available: https://quantumzeitgeist.com/d-wave-ceo-gives-predictions-for-quantum-in-2024/

Swayne, M. [Online]. Available: https://thequantuminsider.com/2023/12/30/looking-back-looking-ahead-quantum-experts-reflect-on-2023-peer-into-2024/

Baccari, F., D. Cavalcanti, P. Wittek, and A. Acín, "Efficient Device-Independent Entanglement Detection for Multipartite Systems", Physical Review X Vol. 7, No. 2, pp. 021042, 2017.

Chen, C., C. Ren, H. Lin, and H. Lu, "Entanglement structure detection via machine learning", Quantum Science and Technology Vol. 6, No., 2021.

Zangi, S.M., J.-L. Li, and C.-F. Qiao, "Entanglement classification of four-partite states under the SLOCC", Journal of Physics A: Mathematical and Theoretical Vol. 50, No. 32, pp. 325301, 2017.

Gharahi, M. and S. Mancini, "Algebraic-geometric characterization of tripartite entanglement", Physical Review A Vol. 104, No. 4, pp. 042402, 2021.

Li, D., "Stochastic local operations and classical communication (SLOCC) and local unitary operations (LU) classifications of n qubits via ranks and singular values of the spin-flipping matrices", Quantum Information Processing Vol. 17, No., 2018.

Zhahir, A.A., S.M. Mohd, M.I.M. Shuhud, B. Idrus, H. Zainuddin, N.M. Jan, and M.R. Wahiddin, "Entanglement Classification for Three-qubit Pure Quantum System using Special Linear Group under the SLOCC Protocol", International Journal of Advanced Computer Science and Applications Vol., No., 2023.

Backens, M., "Number of superclasses of four-qubit entangled states under the inductive entanglement classification", Physical Review A Vol. 95, No., 2017.

Einstein, A., B. Podolsky, and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?", Physical Review Vol. 47, No. 10, pp. 777-780, 1935.

Schrödinger, E., "Discussion of Probability Relations between Separated Systems", Mathematical Proceedings of the Cambridge Philosophical Society Vol. 31, No. 4, pp. 555-563, 1935.

Bell, J.S., "On the Einstein Podolsky Rosen paradox", Physics Physique Fizika Vol. 1, No. 3, pp. 195-200, 1964.

Lian, J.-Y., X. Li, and T.-Y. Ye, "Multi-party semiquantum private comparison of size relationship with d-dimensional Bell states", EPJ Quantum Technology Vol. 10, No. 1, pp. 10, 2023.

Castelvecchi, D., "How ‘spooky’ is quantum physics? The answer could be incalculable", Vol. 577, No., pp. 461-462, 2020.

Makarov, D.N., "Quantum entanglement of photons on free electrons", Results in Physics Vol. 49, No., pp. 106515, 2023.

Zhahir, A.A., S.M. Mohd, M.I. M Shuhud, B. Idrus, H. Zainuddin, N. Mohamad Jan, and M.R. Wahiddin, "Quantum Computing in The Cloud-A Systematic Literature Review", International journal of electrical and computer engineering systems Vol. 15, No. 2, pp. 185-200, 2024.

Matthews, D., "How to get started in quantum computing", Vol. 591, No., pp. 166-167, 2021.

Ivashkin, A., D. Abdurashitov, A. Baranov, F. Guber, S. Morozov, S. Musin, A. Strizhak, and I. Tkachev, "Testing entanglement of annihilation photons", Scientific Reports Vol. 13, No. 1, pp. 7559, 2023.

Huang, X.-J., P.-R. Han, W. Ning, S.-B. Yang, X. Zhu, J.-H. Lü, R.-H. Zheng, H. Li, Z.-B. Yang, K. Xu, C.-P. Yang, Q.-C. Wu, D. Zheng, H. Fan, and S.-B. Zheng, "Entanglement-interference complementarity and experimental demonstration in a superconducting circuit", npj Quantum Information Vol. 9, No. 1, pp. 43, 2023.

Kumari, A. and S. Adhikari, "Classification witness operator for the classification of different subclasses of three-qubit GHZ class", Quantum Information Processing Vol. 20, No. 9, pp. 316, 2021.

Datta, C., S. Adhikari, A. Das, and P. Agrawal, "Distinguishing different classes of entanglement of three-qubit pure states", The European Physical Journal D Vol. 72, No. 9, pp. 157, 2018.

Li, D., "SLOCC classification of n qubits invoking the proportional relationships for spectrums and standard Jordan normal forms", Quantum Information Processing Vol. 17, No. 1, 2017.

Walter, M., D. Gross, and J. Eisert, "Multipartite entanglement",Ed., Wiley-VCH Verlag, pp. 38, 2016.

Wu, Q.-F., "Entanglement Classification via Operator Size: a Monoid Isomorphism", arXiv preprint arXiv:2111.07636 Vol., No., 2022.

Mohd, S.M., B. Idrus, H. Zainuddin, and M. Mukhtar, "Entanglement classification for a three-qubit system using special unitary groups, SU (2) and SU (4)", International Journal of Advanced Computer Science and Applications Vol., No., 2019.

Kraus, B., "Local unitary equivalence and entanglement of multipartite pure states", Physical Review A Vol. 82, No. 3, 2010.

Dietrich, H., W.A. De Graaf, A. Marrani, and M. Origlia, "Classification of four qubit states and their stabilisers under SLOCC operations", Journal of Physics A: Mathematical and Theoretical Vol. 55, No. 9, 2022.

Jaffali, H. and F. Holweck, "Quantum entanglement involved in Grover’s and Shor’s algorithms: the four-qubit case", Quantum Information Processing Vol. 18, No. 5, 2019.

Zha, X., I. Ahmed, D. Zhang, W. Feng, and Y. Zhang, "Stochastic local operations and classical communication invariants via square matrix", Laser Physics Vol. 29, No. 2, 2019.

Aulbach, M., "Symmetric entanglement classes for n qubits", arXiv preprint arXiv:1103.0271 Vol., No., 2011.

Luc, J., "Quantumness of States and Unitary Operations", Foundations of Physics Vol. 50, No. 11, pp. 1645-1685, 2020.

Bennett, C.H., S. Popescu, D. Rohrlich, J.A. Smolin, and A.V. Thapliyal, "Exact and asymptotic measures of multipartite pure-state entanglement", Physical Review A Vol. 63, No. 1, pp. 012307, 2000.

Liu, B., J.-L. Li, X. Li, and C.-F. Qiao, "Local unitary classification of arbitrary dimensional multipartite pure states", Physical review letters Vol. 108, No. 5, pp. 050501, 2012.

Char, P., P.K. Dey, A. Kundu, I. Chattopadhyay, and D. Sarkar, "New monogamy relations for multiqubit systems", Quantum Information Processing Vol. 20, No. 1, pp. 30, 2021.

Ashourisheikhi, S. and S. Sirsi, "Local Unitary Equivalent Classes of Symmetric N-qubit Mixed State", International Journal of Quantum Information Vol. 11, No. 08, pp. 1350072, 2013.

Beckey, J.L., N. Gigena, P.J. Coles, and M. Cerezo, "Computable and Operationally Meaningful Multipartite Entanglement Measures", Physical Review Letters Vol. 127, No. 14, pp. 140501, 2021.

Qi, X., T. Gao, and F. Yan, "The verification of a requirement of entanglement measures", Quantum Information Processing Vol. 20, No. 4, pp. 133, 2021.

Sengupta, K., R. Zibakhsh, E. Chitambar, and G. Gour, "Quantum Bell Nonlocality is Entanglement", arXiv: Quantum Physics Vol., No., 2020.

Chitambar, E., J.I.d. Vicente, M.W. Girard, and G. Gour, "Entanglement manipulation beyond local operations and classical communication", Journal of Mathematical Physics Vol. 61, No. 4, pp. 042201, 2020.

Gharahi, M., S. Mancini, and G. Ottaviani, "Fine-structure classification of multiqubit entanglement by algebraic geometry", Physical Review Research Vol. 2, No. 4, pp. 043003, 2020.

Ritz, C., C. Spee, and O. Gühne, "Characterizing multipartite entanglement classes via higher-dimensional embeddings", Journal of Physics A: Mathematical and Theoretical Vol. 52, No. 33, pp. 335302, 2019.

Eltschka, C. and J. Siewert, "Quantifying entanglement resources", Journal of Physics A: Mathematical and Theoretical Vol. 47, No. 42, pp. 424005, 2014.

Steinhoff, F., "Multipartite states under elementary local operations", Physical Review A Vol. 100, No. 2, pp. 022317, 2019.

Wu, X., H.-Y. Jia, D.-D. Li, Y.-H. Yang, and F. Gao, "N-qudit SLOCC equivalent W states are determined by their bipartite reduced density matrices with tree form", Quantum Information Processing Vol. 19, No. 12, pp. 423, 2020.

Zuppardo, M., R. Ganardi, M. Miller, S. Bandyopadhyay, and T. Paterek, "Entanglement gain in measurements with unknown results", Phys. Rev. A Vol. 99, No. 4, pp. 042319, 2018.

Yu, D.-H. and C.-S. Yu, "Quantifying entanglement in terms of an operational way", Chin. Phys. B Vol. 30, No. 2, pp. 20302-0, 2021.

Ma, X., W. Li, and Y. Gu, "Transformation of a class of pure multipartite entangled states", Results in Physics Vol. 57, No., pp. 107347, 2024.

Wang, S., Y. Shen, X. Liu, H. Zhang, and Y. Wang, "Variational quantum entanglement classification discrimination", Physica A: Statistical Mechanics and its Applications Vol. 637, No., 2024.

Trigg, G.L., "Mathematical Tool for Physicists",Ed., John Wiley & Sons, pp. 686, 2005.

Conway, J.H. and J.G. Thackray, "Atlas of finite groups : maximal subgroups and ordinary characters for simple groups", Mathematics of Computation Vol. 48, No., pp. 441, 1987.

Ziller, W., "Lie Groups. Representation Theory and Symmetric Spaces",Ed., 2010.

Goodman, R. and N.R. Wallach, "Symmetry, Representations, and Invariants",Ed., Springer New York, 2009.

Gour, G. and N. Wallach, "Classification of Multipartite Entanglement of All Finite Dimensionality", Physical review letters Vol. 111, No., pp. 060502, 2013.

Vokos, S., B. Zumino, and J. Wess, "Properties of quantum 2x2 matrices", Vol., No. LAPP-TH--253-89, pp. 11 1989.

Weaver, N., "Mathematical Quantization ", 1st EditionEd., 2001.

Zainuddin, H., P. Toh, N. Mohd Shah, M. Zainy, Z. Zulkarnain, J. Hassan, and Z. Hassan, "No-Go theorems and quantization", Malaysian Journal of Fundamental and Applied Sciences Vol. 3, No., 2014.

Downloads

Published

2024-10-08

How to Cite

Amirul Asyraf Zhahir, Siti Munirah Mohd, Mohd Sham Mohamad, Mohd Ilias M Shuhud, Bahari Idrus, Hishamuddin Zainuddin, & Nurhidaya Mohamad Jan. (2024). Quantum Entanglement and Its Classification Protocols . Malaysian Journal of Science Health & Technology, 10(2), 99–106. https://doi.org/10.33102/mjosht.v10i2.408

Issue

Section

Mathematics