PauliReduce is an option for PauliTrick and other functions. It specifies whether a chain of Pauli matrices should be reduced to at most one matrix by rewriting every pair of matrices in terms of commutator and anticommutator.
Overview, PauliTrick, PauliSimplify.
CSI[i, j, k]
PauliSimplify[%]\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^k
\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^k
CSI[i, j, k]
PauliSimplify[%, PauliReduce -> True]\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^k
\overline{\sigma }^i \bar{\delta }^{jk}-\overline{\sigma }^j \bar{\delta }^{ik}+\overline{\sigma }^k \bar{\delta }^{ij}+i \bar{\epsilon }^{ijk}