Linear Combinations of Pauli Matrix Tensor Products, Frobenius Inner Product, Trace of Matrix

[@JacobShaw-cl3hl]

very well explained

[@Elucyda]

For an n qubit system described by a N=2^n dimensional Hilbert space, the normalization factor for the Frobenius inner product is 1/(2^n).

[@farhadtowfiq6767]

@Elucyda How did you compose The SWAP gate as 1/2(II+XX+YY+ZZ)? What is the intuition behind it?

[@farhadtowfiq6767]

Never mind, I already see the answer. You have to decompose the tensor it is applied to into eigenvectors of X, Y, and Z for terms XX, YY, and ZZ.

[@Jagann]

Is there a way you can prove the coefficients are half times the trace of A2 with Pailu matrix?