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user64620
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Inner function with Kronecker products

I am trying to calculate $\sigma_1 \otimes \sigma_2 + \sigma_2 \otimes \sigma_1$ as a inner product. My attempt

Inner[KroneckerProduct, {PauliMatrix[1], PauliMatrix[2]}, {PauliMatrix[2], PauliMatrix[1]}, Plus] 

does not work. Any idea why?