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On sets of maximally commuting and anticommuting Pauli operators

On sets of maximally commuting and anticommuting Pauli operators In this work, we study the structure and cardinality of maximal sets of commuting and anticommuting Paulis in the setting of the abelian Pauli group. We provide necessary and sufficient conditions for anticommuting sets to be maximal and present an efficient algorithm for generating anticommuting sets of maximum size. As a theoretical tool, we introduce commutativity maps and study properties of maps associated with elements in the cosets with respect to anticommuting minimal generating sets. We also derive expressions for the number of distinct sets of commuting and anticommuting abelian Paulis of a given size. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

On sets of maximally commuting and anticommuting Pauli operators

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021
eISSN
2197-9847
DOI
10.1007/s40687-020-00244-1
Publisher site
See Article on Publisher Site

Abstract

In this work, we study the structure and cardinality of maximal sets of commuting and anticommuting Paulis in the setting of the abelian Pauli group. We provide necessary and sufficient conditions for anticommuting sets to be maximal and present an efficient algorithm for generating anticommuting sets of maximum size. As a theoretical tool, we introduce commutativity maps and study properties of maps associated with elements in the cosets with respect to anticommuting minimal generating sets. We also derive expressions for the number of distinct sets of commuting and anticommuting abelian Paulis of a given size.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Feb 15, 2021

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