Figure 2

Quantum Randomization procedure is a collection of CNOT gates applied to the plaintext qubits with secret key qubits set as control. Such implementation is the quantum counterpart of the classical XOR operation. Indeed, suppose the secret key is \(011\ldots 1\) and the plaintext is \(111\ldots 0\). The result of the XOR operation between the said two bit strings is \(100\ldots 1\). Setting the control qubits as depicted in this figure for \(q_{0} = 0, q_{1} = 1, q_{2} =1, \dots , q_{i-1} =1\) and \(q_{i} = q_{i+1} = q_{i+2} =1, \dots , q_{n-1} = 0\) will produce the state \(|100\dots 1\rangle \), which when measured is precisely the bit-string \(100\dots 1\)