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Invalid coefficients in Quantum Process Tomography of the Hadamard gate

The formula $(3)$ is only true when the basis $\rho_j$ is orthonormal. Indeed, to derive $(3)$, we hit both sides of $(2)$ with $\mathrm{tr}(.\rho_k)$ and use $\mathrm{tr}(\rho_j^\dagger\rho_k)=\...
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