Distinguish Orthogonal Qubits: Test & Impact

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    Differentiating Qubits
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Dragonfall
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Given two arbitrary qubits, is there a test I can do that will always tell orthogonal qubits apart (but may fail if they are not)? Does it necessarily destroy the qubits' states?
 
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I'm a bit rusty with Quantum info.

Qubits are only distinguishable from each other if they are mutually orthogonal. This is because you can only make simutaneous measurement in an orthogonal basis (I think).
 
I'm a little rusty as well - but isn't it just like any other HUP-susceptible quantum object - if you can differentiate the states, you've destroyed the states?
 
Is it possible to turn a qubit into an orthogonal one without measuring first? Turn it 90 degrees, so to speak.