Bell state

One of the four following states:

∣ Φ^{+} ⟩ = \frac{1}{2} (∣ 00 ⟩ + ∣ 11 ⟩) ∣ Φ^{-} ⟩ = \frac{1}{2} (∣ 00 ⟩ - ∣ 11 ⟩) ∣ Ψ^{+} ⟩ = \frac{1}{2} (∣ 01 ⟩ + ∣ 10 ⟩) ∣ Ψ^{-} ⟩ = \frac{1}{2} (∣ 01 ⟩ - ∣ 10 ⟩)

(22)

When unqualified as in "the Bell state", it generally just means

∣ Φ^{+} ⟩

The Bell states are entangled and non-separable. Intuitively, we can see that when we measure that state, the values of the first and second bit are strictly correlated. This is the hallmark of quantum computation: making up states where qubits are highly correlated to match a specific algorithmic answer, and opposed to uniformly random noise. For example, the Bell state circuit is a common hello world, e.g. it is used in the official Qiskit hello world.

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