How To Create Bell States: A Mathematical Lesson

Let's explore how to create Bell states using other qubits and quantum gates.

Photograph of John Stewart Bell, a physicist best known for formulating Bell’s theorem, which demonstrated that quantum entanglement cannot be explained by any local hidden variable theory. (Source: Wikipedia)

Bell states are maximally entangled two-qubit states, named after the physicist John Stewart Bell.

There are four Bell states, and their Dirac notations are shown below:

1. Φ⁺ (Phi plus)

2. Φ⁻ (Phi minus)

3. Ψ⁺ (Psi plus)

4. Ψ⁻ (Psi minus)

In the last lesson, we discussed Bell states in depth. In this lesson, we will talk about how to create them.

---

Creating The Phi Plus Bell State

We start with a two-qubit system |00> (which can also be written as the tensor product |0⟩ ⊗ |0⟩).