by Ciro Santilli (@cirosantilli, 37)
One of the four following states:
(1)
When unqualified as in "the Bell state", it generally just means .
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.
A quantum circuit which when fed with input produces the Bell state.
Figure 1.
Quantum circuit that generates the Bell state
. Source.
The fundamental intuition for this circuit is as follows.
First the Hadamard gate makes the first qubit be in a 50/50 state.
Then, the CNOT gate gets controlled by that 50/50 value, and the controlled qubit also gets 50/50 chance as a result.
However, both qubits are now entangled: the result of the second qubit depends on the result of the first one. Because:

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Bell state by Wikipedia Bot 0 1970-01-01
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A Bell state is a specific type of quantum state that represents maximal entanglement between two qubits. There are four Bell states, and they form the basis of the two-qubit quantum system. The four Bell states are: 1. \(|\Phi^+\rangle = \frac{1}{\sqrt{2}} (|00\rangle + |11\rangle)\) 2.
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