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Published equation contexts

U(∣ψ⟩⊗∣0⟩)=∣ψ⟩⊗∣ψ⟩U\left(|\psi\rangle \otimes |0\rangle\right) = |\psi\rangle \otimes |\psi\rangle

Why this formula appears here

The classical repetition code is the first thing anyone reaches for, and quantum mechanics forbids it. A unitary machine that maps an arbitrary unknown state alongside a blank register onto two copies, U(∣ψ⟩⊗∣0⟩)=∣ψ⟩⊗∣ψ⟩U\left(|\psi\rangle \otimes |0\rangle\right) = |\psi\rangle \otimes |\psi\rangle . cannot exist for all |ψ\psi⟩\rangle , because unitarity preserves inner products and the required map does not. Wootters and Zurek established the point in 1982, in a paper whose title remains the cleanest statement of it [ 1 ] . There is no backup copy, no parity check computed by reading the data, no majority vote over three inspected replicas.

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ψ\psi

Symbol psi

psi is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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Published contexts (1)

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U(∣ψ⟩⊗∣0⟩)=∣ψ⟩⊗∣ψ⟩,U\left(|\psi\rangle \otimes |0\rangle\right) = |\psi\rangle \otimes |\psi\rangle ,

Equation 1 · Quantum Information

Error Correction Is the Whole Problem in Quantum Computing

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The classical repetition code is the first thing anyone reaches for, and quantum mechanics forbids it. A unitary machine that maps an arbitrary unknown state alongside a blank register onto two copies, U(∣ψ⟩⊗∣0⟩)=∣ψ⟩⊗∣ψ⟩U\left(|\psi\rangle \otimes |0\rangle\right) = |\psi\rangle \otimes |\psi\rangle . cannot exist for all |ψ\psi⟩\rangle , because unitarity preserves inner products and the required map does not. Wootters and Zurek established the point in 1982, in a paper whose title remains the cleanest statement of it [ 1 ] . There is no backup copy, no parity check computed by reading the data, no majority vote over three inspected replicas.

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