# Tag Info

## Hot answers tagged trace-distance

2

For the way round that you've got your inequalities, I don't think there's much that can be said. To see why, let's consider the first expression $$\|U-V\|_1=\text{Tr}(\sqrt{2I-VU^\dagger-UV^\dagger}).$$ Now, $VU^\dagger$ is a unitary, and hence as a spectral decomposition. Let the eigenvectors be $|\lambda_i\rangle$ with eigenvalues $e^{i\lambda_i}$. \$UV^\...

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