On sets of maximally commuting and anticommuting Pauli operators

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.

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Acknowledgements

The authors would like to thank the anonymous reviewer whose suggestions helped to greatly improve the paper. The authors would also like to thank Sergey Bravyi, Kristan Temme, and Ted Yoder for useful discussions. R.S. would like to thank IBM T.J. Watson Research Center for facilitating the research.

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Correspondence to Ewout van den Berg.

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Sarkar, R., van den Berg, E. On sets of maximally commuting and anticommuting Pauli operators. Res Math Sci 8, 14 (2021). https://doi.org/10.1007/s40687-020-00244-1

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Keywords

  • Pauli operators
  • Commutativity
  • Maximal subgroups