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Magic informationally complete POVMs with permutations.

Michel Planat1, Zafer Gedik2

  • 1Université de Bourgogne/Franche-Comté, Institut FEMTO-ST CNRS UMR 6174, 15 B Avenue des Montboucons, 25044 Besançon, France.

Royal Society Open Science
|October 10, 2017
PubMed
Summary
This summary is machine-generated.

Magic states, a key component for universal quantum computation, can define informationally complete POVMs when acting on generalized Pauli groups. These POVMs reveal finite geometries and connections to quantum contextuality in various dimensions.

Keywords:
finite geometryinformationally complete POVMsmagic statespermutation groupsquantum contextuality

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Area of Science:

  • Quantum Information Theory
  • Quantum Computation
  • Finite Geometry

Background:

  • Eigenstates of permutation gates are crucial for quantum computation, being either stabilizer or magic states.
  • Magic states are essential for achieving universal quantum computation beyond stabilizer circuits.

Purpose of the Study:

  • To investigate the properties of magic states within the generalized Pauli group framework.
  • To demonstrate that specific magic states define informationally complete POVMs.
  • To explore the geometric and contextual properties of these informationally complete POVMs.

Main Methods:

  • Analysis of eigenstates of permutation gates.
  • Application of magic states to the generalized Pauli group.
  • Investigation of informationally complete POVMs in dimensions 2-12.
  • Examination of projector products and connections to quantum contextuality.

Main Results:

  • A subset of magic states, when acting on the generalized Pauli group, forms informationally complete POVMs.
  • These POVMs exhibit simple finite geometries in their projector products across dimensions 2-12.
  • For dimensions 4, 8, and 9, these POVMs show relationships to two-qubit, three-qubit, and two-qutrit contextuality.

Conclusions:

  • Magic states play a vital role in constructing informationally complete POVMs.
  • The study reveals a deep connection between quantum information processing, finite geometries, and quantum contextuality.
  • These findings contribute to understanding the structure and capabilities of quantum computational resources.