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

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## Abstract

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) |
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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 09:42 |

Last Modified: | 28 Dec 2018 09:43 |

URI: | http://eprints.iiserkol.ac.in/id/eprint/788 |

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