= Unitary invariance of trace distance and fidelity
For any unitary $U$, the unique <positive square root of an operator> obeys $\sqrt{UAU^\dagger}=U\sqrt A U^\dagger$. Conjugating the <positive operators> appearing in <trace distance> and <quantum fidelity> therefore conjugates their square roots. Cyclicity of the <trace> removes the unitary factors, proving invariance of both quantities under simultaneous unitary transformations of the states.
// Target: quantum-information-theory.bigb
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