What if we have multiple qubits? The following equation denotes the state of a two-qubit system.

∣ψ⟩=α∣00⟩+β∣01⟩+γ∣10⟩+δ∣11⟩=[αβγδ]|\psi\rangle=\alpha|00\rangle+\beta|01\rangle+\gamma|10\rangle+\delta|11\rangle=\begin{bmatrix}\alpha \\ \beta \\ \gamma \\ \delta \end{bmatrix}

The two-qubit system can be in four different states. Each state has an amplitude, too.

We’ve already specified a two-qubit system two and the Bloch spheres side by side in the lesson Two Different Qubit States. Qubit 0 is in state ∣0⟩−∣1⟩2\frac{|0\rangle-|1\rangle}{\sqrt{2}} and qubit 1 is in state −∣0⟩+∣1⟩2\frac{-|0\rangle+|1\rangle}{\sqrt{2}}.

Let’s have a look at the phases of the four states of this system.

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