Schmidt Decomposition in Multipartite Hilbert Space

Das, Spandan (2018) Schmidt Decomposition in Multipartite Hilbert Space. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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In this report, we discuss a necessary and sufficient condition for the existence of Schmidt decomposition of a pure state in a multipartite Hilbert space. Schmidt decomposition exists for any pure state in a bipartite Hilbert space. It is extremely useful since it reduces the number of terms needed to represent a pure state using orthonormal bases of the respective parts. However, for 3 or more partite Hilbert spaces, Schmidt decomposition does not exist in general for an arbitrary pure state. In this thesis, we derive a condition that states whether a state in an n-partite Hilbert space is Schmidt-decomposable or not, i.e., whether we can represent it through the orthonormal bases of the respective parts using less number of terms that is required in general.

Item Type: Thesis (Masters)
Additional Information: Supervisors: Dr. Goutam Paul and Dr. Swarnendu Datta
Uncontrolled Keywords: Hilbert Space; Linear Algebra; Multipartite Hilbert Spaces; Quantum Mechanics; Schmidt Decomposition
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Department of Mathematics and Statistics
Depositing User: IISER Kolkata Librarian
Date Deposited: 28 Dec 2018 04:12
Last Modified: 28 Dec 2018 04:13

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