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\title{Quantum Entanglement and Its Applications in Quantum Computing}
\author{Jane Smith\\University of Science}
\date{\today}

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\begin{abstract}
This paper explores the phenomenon of quantum entanglement and its role in quantum computing. We discuss the fundamental principles of entanglement, review recent experimental advances, and analyze potential applications in quantum algorithms and information processing.
\end{abstract}

\section{Introduction}
Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles interact in ways such that the quantum state of each particle cannot be described independently of the others. Instead, a quantum state must be described for the system as a whole.

\section{Theoretical Framework}
The mathematical formulation of entanglement relies on the tensor product structure of quantum mechanics. For a system of two qubits, the general state can be written as:

\begin{equation}
|\psi\rangle = \alpha|00\rangle + \beta|01\rangle + \gamma|10\rangle + \delta|11\rangle
\end{equation}

where $\alpha, \beta, \gamma, \delta$ are complex coefficients with $|\alpha|^2 + |\beta|^2 + |\gamma|^2 + |\delta|^2 = 1$.

\section{Experimental Verification}
Recent experiments have conclusively demonstrated the non-local nature of quantum entanglement, confirming Bell's inequality violations \cite{aspect1982}.

\begin{thebibliography}{9}
\bibitem{aspect1982}
Aspect, A., Dalibard, J., \& Roger, G. (1982). 
\textit{Experimental Test of Bell's Inequalities Using Time-Varying Analyzers}. 
Physical Review Letters, 49(25), 1804-1807.
\end{thebibliography}

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