Commutators and Anticommutators

Gianfausto Dell’Antonio, Sergio Doplicher, David Pierre Ruelle

A. Cordesse

Rahul Sarkar, E. van den Berg

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.

Istok P. Mendaš, P Milutinovic

The generalization of the Baker-Hausdorff lemma and its anticommutator analogue is formulated. Additionally, the anticommutator analogues of several well known operator identities involving repeated commutators are derived. It is pointed out that these are more convenient for application whenever the operators in question satisfy simpler repeated anticommutator relations (and, in particular, when they anticommute) than the repeated commutator relations. The diagonalization of two spin-1 Hamiltonians, in which the anticommutator analogue of the Baker-Hausdorff lemma is used to good advantage, is presented.