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The two qubits are initalized in the state

Measurement

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After the two Hadamard operators, the two-qubit state becomes:

The unitary operator Uf encodes the function f into the state of the qubits

After another Hadamard operator on each qubit, the output state depends on  the characteristic of the function f:

0 or 1

A measurement of the first qubit will then determinewhether the function f is constant or balanced. 

This is how we can tell whether the function is  constant or balanced.