rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Mutually unbiased unitary bases and its context in uncertainty relation for unitary operators
  name:
    name part: Rinie Narinie Mohd Nasir
    role:
      role term: creator
    role:
      role term: author
  name:
    name part: Jesni Shamsul Shaari
    role:
      role term: degree supervisor
  name:
    name part: Stefano Mancini
    role:
      role term: degree supervisor
  name:
    name part: International Islamic University Malaysia
    name part: Kulliyyah of Science
  type of resource: text
  genre: theses
  genre: Theses, IIUM local
  origin info:
    place:
      place term: my
    date issued: 2021
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xvii, 96 leaves : 30 cm.
  abstract: Analogous to Mutually Unbiased Bases (MUB) for d-dimensional Hilbert space, H_d capturing the notion of equiprobable transition between states in one basis to another, we consider a similar notion for some subspace of linear operators instead. Working mainly in terms of matrices, the notion of Mutually Unbiased Unitary Bases (MUUB) of M(d,C) can be understood in terms of the equiprobable guess of a unitary operator in one basis for that in another. MUUBs has in fact shown to be useful in specific quantum key distribution (QKD) protocols, namely bidirectional QKD protocols akin to the role of MUBs for prepare and measure QKD schemes like the well-known BB84 protocol. The MUUB structure is strongly related to the notion of MUBs consisting only of maximally entangled states of space H_d ⨂▒H_d or, mutually unbiased maximally entangled bases (MUMEBS). The two are essentially equivalent though much remains to be explored. In fact, for a d^2-dimensional space of M(d,C), while it is known that the maximal numbers that MUUBs can have is d^2-1, there is no known recipe for constructing the maximal number of such bases. It is not even known if such a number may even be achieved for any d Focusing on the case for d being the prime numbers, we show that the minimal number for MUUBs is 3 and approaches its maximal d^2-1 for very large values of d. We further provide a numerical recipe in constructing MUUBs which gives us an explicit construction for the maximal number of MUUBs for subspaces of M(3,C) and M(2,C). Despite the possible use of the numerical search for any dimension, it quickly becomes inefficient as d grows. For a more analytical solution, we turn our focus to the case of some d-dimensional subspace for any prime d and report on the maximal number of MUUBs for such a subspace. By constructing monoids based on the underlying sets of H_d and a subspace of M(d,C), an isomorphism between the monoids lead to an important theorem for constructing d MUUBs, i.e. the maximal …
  target audience: specialized
  note: by Rinie Narinie Binti Mohd Nasir
  note: Abstracts in English and Arabic.
  note: "A thesis submitted in fulfilment of the requirement for the degree of Doctor of Philosophy in Computational and Theoretical Sciences." --On title page.
  note: Thesis (Ph.D)--International Islamic University Malaysia, 2021.
  note: Includes bibliographical references (leaves 93-96).
  subject:
    geographic code: a-my---
  identifier: http://studentrepo.iium.edu.my/handle/123456789/11263
  record info:
    record content source: UIAM
    record creation date: 230302
    language of cataloging:
      language term: eng