 Suppose we attempt to use a CNOT gate to copy an unknown qubit state. Since we are now proposing to regard the CNOT gate as a device for processing quantum states, the evolution from input states to output states must be effected by a physical quantum transformation. Quantum transformations are linear on the linear state space of qubits. Linearity of the state space means that any sum or superposition with coefficients \(c_0, c_1\) of two qubit states in the state space is also a qubit state in the state space. Linearity of the transformation requires that the transformation should take a qubit state represented by the sum of two qubit states to a new qubit state that is the sum of the transformed qubit states. If the CNOT gate succeeds in copying two orthogonal qubit states, represented as \(\ket{0},\ket{1}\), it cannot succeed in copying a general linear superposition of these qubits. Since the gate functions linearly, it must instead produce a state that is a linear superposition of the outputs obtained for the two orthogonal qubit states. That is to say, the output of the gate will be represented by a quantum state that is a sum of two terms, where the first term represents the output of the control and target for the first qubit state, and the second term represents the output of the control and target for the second orthogonal qubit state. This could be expressed as \(c_0 \ket{0} \ket{0}\) + \(c_1 \ket{1} \ket{1}\), which is an entangled state (unless \(c_0\) or \( c_1\) is zero) rather than the output that would be required by a successful copying operation (where the control and target each outputs the superposition qubit state \(c_0 \ket{0}\) + \(c_1 \ket{1}\)).