Let us make things a bit more complex. We are now able to perform operations in the 2-dimensional 𝐶² space. In the previous discussion, we measured 2-qubit states in this defined space. Now, we will measure 3-qubit states and, if necessary, generalize what we have learned to discuss n-qubit states.

When measuring 3-qubit states, specific operators are used for each qubit. For instance, let us define an operator 𝐴. To measure the relevant qubit using the 𝐴 operator, the following operator applications need to be performed:

– 𝐴 ⊗ 𝐼 ⊗ 𝐼 for the 1st qubit

– 𝐼 ⊗ 𝐴 ⊗ 𝐼 for the 2nd qubit

– 𝐼 ⊗ 𝐼 ⊗ 𝐴 for the 3rd qubit

We previously discussed that the 𝐼 operator is the identity operator. While performing these measurements, we are referring to non-superposed states such as |𝑥⟩|𝑦⟩|𝑧⟩, which take simple and definite values. In these types of measurements, each qubit represents a clear value, either |0⟩ or |1⟩.

If we generalize these expressions, we can state the following based on the operator used:

• The operator applied to |0⟩|0⟩|0⟩ always yields a result of 0.
• The operator applied to |0⟩|0⟩|1⟩ yields 1 if measuring the 3rd qubit; otherwise, it yields 0.
• The operator applied to |1⟩|1⟩|1⟩ measures 1 in all cases.

This measurement method can be generalized to systems with 1, 2, and 3 qubits for the measurement of non-superposed states. In each case, the application of the operator is calculated based on the value of the given qubit and the measurement result.