Function to generate the Kronecker Product of a variable number of Pauli Matrices

Question

I would like to implement a function with variable numbers of arguments that generates

$\sigma_{j_1}\otimes\ldots \otimes\sigma_{j_L}$

where $\otimes$ is the Kronecker Product and $\sigma_j$ are the PauliMatrix[j]. I realize this function with

f[val__] := First@With[{lvar = Table[Symbol["j" <> ToString@k], {k, 
   Length@val}]}, (KroneckerProduct @@ 
  PauliMatrix /@ lvar) /. {MapThread[#1 -> #2 &, {lvar, val}]}]

For instance for obtaining $\sigma_1\otimes\sigma_1\otimes \sigma_2$ I write

f[{1, 1, 2}] 

It there a more easier way to do it?

Answer 1

Since PauliMatrix is Listable, you can simplify your definition to:

Clear[f2]
f2[list_List] := KroneckerProduct @@ PauliMatrix[list]

f[{1, 1, 2}] == f2[{1, 1, 2}]
(* True *)