Bell state

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One of the four following states:

$$
\begin{aligned}
\ket{\Phi^+} &= \frac{1}{\sqrt{2}} (\ket{00} &+ \ket{11})
\ket{\Phi^-} &= \frac{1}{\sqrt{2}} (\ket{00} &- \ket{11})
\ket{\Psi^+} &= \frac{1}{\sqrt{2}} (\ket{01} &+ \ket{10})
\ket{\Psi^-} &= \frac{1}{\sqrt{2}} (\ket{01} &- \ket{10})
\end{aligned}
$$

When unqualified as in "the Bell state", it generally just means $\ket{\Phi^+}$.

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>.


 Bell state