Matriks Koefisien bagi Ukuran Keterbelitan Keadaan Dua dan Tiga Qubit

Pingki, Tamara (2026) Matriks Koefisien bagi Ukuran Keterbelitan Keadaan Dua dan Tiga Qubit. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Keterbelitan kuantum (\textit{quantum entanglement}) merupakan salah satu sumber daya fundamental dalam pemrosesan informasi kuantum. Meskipun klasifikasi keterbelitan pada sistem bipartit telah dipahami dengan baik, identifikasi kelas keterbelitan pada sistem multipartit masih menjadi permasalahan yang kompleks akibat meningkatnya jumlah konfigurasi keterbelitan seiring bertambahnya jumlah qubit. Penelitian ini bertujuan untuk merumuskan suatu kerangka teoritis berbasis matriks koefisien guna mengidentifikasi dan mengklasifikasikan keterbelitan pada sistem dua dan tiga qubit. Metode penelitian dilakukan secara analitik melalui formulasi matriks koefisien yang dibangun dari amplitudo keadaan kuantum. Untuk sistem dua qubit, diperoleh formulasi matriks koefisien berupa $\mathrm{Tr},\rho \tilde{\rho} = 4 \det \rho_A$, sedangkan untuk sistem tiga qubit diperoleh hubungan $\mathrm{Tr}\,\rho_{AB} \tilde{\rho}_{AB}= 4 |\det C_{AB0}|^2 + 4 |\det C_{AB1}|^2 + 2 (\det C_{AB0}^1 + \det C_{AB1}^0)(\det C^{*1}_{AB0} + \det C^{*0}_{AB1})$. Formulasi tersebut kemudian diterapkan pada berbagai keadaan kuantum dua dan tiga qubit untuk menentukan distribusi keterbelitannya. Hasil penelitian ini menunjukkan bahwa pendekatan berbasis matriks koefisien dapat digunakan sebagai metode alternatif yang lebih sederhana dan efisien untuk mengkarakterisasi kelas keterbelitan pada sistem dua dan tiga qubit.
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Quantum entanglement (\textit{quantum entanglement}) is a fundamental resource in quantum information processing. Although the classification of entanglement in bipartite systems is well understood, identifying entanglement classes in multipartite systems remains a complex problem due to the increasing number of entanglement configurations as the number of qubits increases. This study aims to formulate a coefficient matrix-based theoretical framework to identify and classify entanglement in two- and three-qubit systems. The research method is carried out analytically through the formulation of a coefficient matrix constructed from the amplitudes of quantum states. For a two-qubit system, the coefficient matrix formulation is $\mathrm{Tr},\rho \tilde{\rho} = 4 \det \rho_A$, while for a three-qubit system, the relationship is $\mathrm{Tr}\,\rho_{AB} \tilde{\rho}_{AB}= 4 |\det C_{AB0}|^2 + 4 |\det C_{AB1}|^2 + 2 (\det C_{AB0}^1 + \det C_{AB1}^0)(\det C^{*1}_{AB0} + \det C^{*0}_{AB1})$. This formulation is then applied to various two- and three-qubit quantum states to determine their entanglement distributions. The results of this study show that the coefficient matrix-based approach can be used as a simpler and more efficient alternative method to characterize entanglement classes in two- and three-qubit systems.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Coefficient Matrix, Entanglement,Two-Qubit, Three-Qubit, Matriks Koefisien, Keterbelitan, Dua Qubit, Tiga Qubit
Subjects:	Q Science > QC Physics > QC174.17.Q38 Quantum teleportation
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Physics > 45101-(S2) Master Thesis
Depositing User:	Tamara Pingki
Date Deposited:	03 Aug 2026 07:45
Last Modified:	03 Aug 2026 07:45
URI:	http://repository.its.ac.id/id/eprint/142401

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