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I want define a function of n variables as follows $$f(x_1, ..., x_n)= KroneckerProduct[\sigma^{x_1}, ..., \sigma^{x_n}]$$ where $\sigma^{x_i}=PauliMatrix[x_i]$. Given a number $n$, I can explicitly write down an expression. For example, for $n=3$, I can write down

f[i1_, i2_, i3_] :=KroneckerProduct[PauliMatrix[i1], PauliMatrix[i2],PauliMatrix[i3]]; 

However, how to write down a generic expression in terms of arbitrary $n$, so that I don't have to rewrite the expression for every choice of $n$? Thanks!

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f[i__] := KroneckerProduct @@ PauliMatrix[{i}]

f[1, 2, 3] == KroneckerProduct[PauliMatrix[1], PauliMatrix[2], PauliMatrix[3]]
(*    True    *)

Do you need special cases for zero or one Pauli matrix, or do these cases never occur for you?

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  • $\begingroup$ Thank you Roman! Zero and One Pauli matrix are not within my consideration. So it should be fine. $\endgroup$
    – user34104
    Jun 1 at 10:19

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