Why must the value of a qubit in quantum computing remain secret? -

i've read time , again, dig through available literature, in quantum computing, smallest unit of value--a qubit--must remain "secret" or unknown until such time measured. in stackoverflow, read that, "in order qubit work one, state has secret rest of physical universe, not you. has secret wisps of air, nearby atoms, etc. on other hand, qubits useful quantum computer, there has way manipulate them while keeping state secret. otherwise quantum randomness or quantum coherence wrecked" (source: does know "quantum computing" is?, answered greg kuperberg). notion of the secrecy of qubit went beyond i've read far, nonetheless, why should be...i mean, explains , justifies strange property--this secrecy or unmeasurability of qubit? answer question me start making mental transition classical computing machines.

it's because quantum stuff interferes if every detail everywhere ends same.

for example, hadamard operation h sends state |0⟩ √½|0⟩+√½|1⟩ , state |1⟩ √½|0⟩-√½|1⟩.

h |0⟩ = √½|0⟩ + √½|1⟩ h |1⟩ = √½|0⟩ - √½|1⟩ 

a neat thing h is own inverse: if apply twice, undoes itself.

h h |0⟩ = h (√½|0⟩ + √½|1⟩)         = √½ h |0⟩ + √½ h |1⟩         = √½ (√½|0⟩ + √½|1⟩) + √½ (√½|0⟩ - √½|1⟩)         = ½ |0⟩ + ½|1⟩ + ½|0⟩ - ½|1⟩         = (½+½) |0⟩ + (½-½) |1⟩         = |0⟩  h h |1⟩ = h (√½|0⟩ - √½|1⟩)         = √½ h |0⟩ - √½ h |1⟩         = √½ (√½|0⟩ + √½|1⟩) - √½ (√½|0⟩ - √½|1⟩)         = ½ |0⟩ + ½|1⟩ - ½|0⟩ + ½|1⟩         = (½-½) |0⟩ + (½+½) |1⟩         = |1⟩ 

but consider happens if, between 2 hadamards, use controlled-not attempt copy qubit-being-hadamarded's value onto second qubit.

even though use qubit control, own-inverse property breaks:

h₁ c₁not₂ h₁ |00⟩ = h₁ c₁not₂ h₁ |0⟩⊗|0⟩                   = h₁ c₁not₂ (h|0⟩)⊗|0⟩                   = h₁ c₁not₂ (√½|0⟩ + √½|1⟩)⊗|0⟩                   = h₁ c₁not₂ (√½|00⟩ + √½|10⟩)                   = h₁ (√½|00⟩ + √½|11⟩)                   = √½ h₁ |00⟩ + √½ h₁ |11⟩                   = √½ (h|0⟩)⊗|0⟩ + √½ (h|1⟩)⊗|1⟩                   = √½ (√½|0⟩ + √½|1⟩)⊗|0⟩ + √½ h (√½|0⟩ - √½|1⟩)⊗|1⟩                   = ½|00⟩ + ½|10⟩ + ½|01⟩ - ½|11⟩ 

the second qubit adds more room state space, , cnot moves of our state room. instead of computation folding states in on cause destructively interference they... kinda spread out.

without destructive interference, might flipping coins instead of rotating qubits. managing effect important in quantum computation.

you can try example in toy circuit simulator quirk, has inline state displays: