The Quantum Entanglement Simulation in Multipartite Systems Using MATLAB

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.