# How can you construct the different two-qubit Bell states?

How can you construct the different Bell states? For example $$\frac{|01⟩-|10⟩}{\sqrt{2}}$$

Firstly construct following circuit:

Different Bell states are created according to input to the circuit follwingly:

• input $$|00\rangle$$, output: $$|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$$
• input $$|10\rangle$$, output: $$|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle)$$
• input $$|01\rangle$$, output: $$|\psi\rangle = \frac{1}{\sqrt{2}}(|01\rangle + |10\rangle)$$
• input $$|11\rangle$$, output: $$|\psi\rangle = \frac{1}{\sqrt{2}}(|01\rangle - |10\rangle)$$

By a combination of Hadamard Gate and CNOT Gate.