International Journal of New Chemistry
ISC, DOAJ, CAS, Google Scholar......

The Quantum Entanglement Simulation in Multipartite Systems Using MATLAB

Document Type : Research Paper

Author

Fatemeh Amiri

Assistant Professor, Department of Physics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran

10.22034/ijnc.2025.722059
Abstract
Quantum entanglement is a fundamental phenomenon in quantum mechanics, playing a crucial role in advanced technologies such as quantum computing, quantum communication, and cryptography. This study explores the entanglement properties of two prominent multipartite quantum states, the GHZ (Greenberger-Horne-Zeilinger) state and the W state, using MATLAB for simulation and analysis. The GHZ state is characterized by perfect correlations among particles but is highly sensitive to particle loss, whereas the W state exhibits a distributed entanglement structure, maintaining partial entanglement even when a particle is lost. To analyze these states, key entropic measures, including von Neumann entropy and Tsallis-2 entropy, were employed to quantify the purity and entanglement of the quantum states. The results show that both states are pure, with von Neumann and Tsallis-2 entropy values close to zero, and exhibit maximal entanglement as confirmed by concurrence metrics. Additionally, a continuous transition between GHZ and W states was simulated to observe dynamic changes in entanglement, revealing significant reductions during intermediate states. This study demonstrates the effectiveness of MATLAB in evaluating multipartite entanglement and highlights the unique properties of GHZ and W states, providing valuable insights for the development of robust quantum technologies.

Keywords

Quantum Entanglement
GHZ State
W State
Entropy Metrics
Quantum Computing

Subjects

[1]        R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, "Quantum entanglement," Reviews of modern physics, vol. 81, no. 2, pp. 865-942, 2009.
[2]        M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information. Cambridge university press, 2010.
[3]        D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, "Bell’s theorem without inequalities," American Journal of Physics, vol. 58, no. 12, pp. 1131-1143, 1990.
[4]        R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Physical review letters, vol. 86, no. 22, p. 5188, 2001.
[5]        T. Yu and J. Eberly, "Sudden death of entanglement," Science, vol. 323, no. 5914, pp. 598-601, 2009.
[6]        O. Gühne and G. Tóth, "Entanglement detection," Physics Reports, vol. 474, no. 1-6, pp. 1-75, 2009.
[7]        C. Tsallis, "Possible generalization of Boltzmann-Gibbs statistics," Journal of statistical physics, vol. 52, pp. 479-487, 1988.
[8]        M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, "Experimental realization of a three-qubit entangled W state," Physical review letters, vol. 92, no. 7, p. 077901, 2004.
[9]        I. Frérot, F. Baccari, and A. Acín, "Unveiling quantum entanglement in many-body systems from partial information," PRX Quantum, vol. 3, no. 1, p. 010342, 2022.
[10]      Z.-H. Ma, Z.-H. Chen, J.-L. Chen, C. Spengler, A. Gabriel, and M. Huber, "Measure of genuine multipartite entanglement with computable lower bounds," Physical Review A—Atomic, Molecular, and Optical Physics, vol. 83, no. 6, p. 062325, 2011.
[11]      Y. Luo, T. Tian, L.-H. Shao, and Y. Li, "General monogamy of Tsallis q-entropy entanglement in multiqubit systems," Physical Review A, vol. 93, no. 6, p. 062340, 2016.
[12]      M. K. Vijayan, A. P. Lund, and P. P. Rohde, "A robust W-state encoding for linear quantum optics," Quantum, vol. 4, p. 303, 2020.
[13]      A. Bernal, J. Casas, and J. M. Moreno, "Entanglement and entropy in multipartite systems: a useful approach," Quantum Information Processing, vol. 23, no. 2, p. 56, 2024.
[14]      F. Delgado and M. Enríquez, "Quantum Entanglement and State-Transference in Fenna–Matthews–Olson Complexes: A Post-Experimental Simulation Analysis in the Computational Biology Domain," International Journal of Molecular Sciences, vol. 24, no. 13, p. 10862, 2023.
[15]      L. Palma Torres, M. Á. Solís-Prosser, O. Jiménez, E. S. Gómez, and A. Delgado, "Optimal High-Dimensional Entanglement Concentration for Pure Bipartite Systems," Micromachines, vol. 14, no. 6, p. 1207, 2023.
[16]      M. Navascués, E. Wolfe, D. Rosset, and A. Pozas-Kerstjens, "Genuine network multipartite entanglement," Physical Review Letters, vol. 125, no. 24, p. 240505, 2020.
[17]      Y. Zhong et al., "Deterministic multi-qubit entanglement in a quantum network," Nature, vol. 590, no. 7847, pp. 571-575, 2021.
[18]      B.-H. Wang, "Internal boundary between entanglement and separability within a quantum state," IEEE Transactions on Information Theory, vol. 69, no. 1, pp. 251-261, 2022.
[19]      Y.-J. Luo, J.-M. Liu, and C. Zhang, "Detecting genuine multipartite entanglement via machine learning," Physical Review A, vol. 108, no. 5, p. 052424, 2023.
[20]      G.-Z. Pan, M. Yang, J. Zhou, H. Yuan, C. Miao, and G. Zhang, "Quantifying entanglement for unknown quantum states via artificial neural networks," Scientific Reports, vol. 14, no. 1, p. 26267, 2024.
[21]      R. Li et al., "Entanglement structure detection via computer vision," Physical Review A, vol. 110, no. 1, p. 012448, 2024.
[22]      Y.-C. Lai, H. Lin, Y.-H. Chen, Y.-L. Hsiao, and L.-C. Chen, "Selecting and Developing a Quantum Internet Simulator for the Needs of New Audience: Practices and Considerations," IEEE Access, 2024.
[23]      Y.-J. Luo, X. Leng, and C. Zhang, "Genuine multipartite entanglement verification with convolutional neural networks," Physical Review A, vol. 110, no. 4, p. 042412, 2024.
[24]      A. Slaoui, N. Ikken, L. B. Drissi, and R. A. Laamara, "Quantum Communication Protocols: From Theory to Implementation in the Quantum Computer," 2023.
[25]      M.-O. Renou et al., "Quantum theory based on real numbers can be experimentally falsified," Nature, vol. 600, no. 7890, pp. 625-629, 2021.
International Journal of New Chemistry
Volume 12, Issue 5
Spring 2025
Pages 922-949

Home

Reviewers