Maximal sets of anticommuting (similarly for commuting) Pauli operators are characterized by the property that any other Pauli not in the set commutes with at least one of the Paulis in the maximal set. In this talk, I will give necessary and sufficient conditions for sets of Paulis to be maximally anticommuting (or commuting). The commuting case has recently found some uses, but they are relatively easy to characterize. However, the maximally anticommuting sets are much more richer in structure than their commuting counterparts, and it would be nice to find use cases for them (which is part of the objective of giving this talk). I will also present a randomized algorithm that runs in polynomial time (in number of qubits) that can extend a non-maximal anticommuting set to its largest size 2n+1, on n qubits.
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