Bell state

A Bell state refers to one of four specific, maximally entangled quantum states involving two qubits. When two particles are in a Bell state, measuring the state of one particle instantly determines the state of the other, regardless of the distance between them. They are the quintessential example of quantum entanglement.

Bell states are the foundational building blocks for many quantum information protocols, including quantum teleportation and superdense coding. They demonstrate quantum entanglement, a phenomenon that Albert Einstein famously dismissed as 'spooky action at a distance.' Their physical realization paved the way for modern quantum computing.

In a laboratory setting, Bell states are often created by firing a laser through a specific type of nonlinear crystal to produce pairs of entangled photons. In a quantum computer, they can be generated by applying a Hadamard gate to one qubit, followed by a Controlled-NOT (CNOT) gate involving a second qubit. This process forces the two qubits into an inseparable quantum link.

Bell's Theorem, formulated by physicist John Stewart Bell in 1964, proves that no physical theory based on local hidden variables can ever reproduce all the predictions of quantum mechanics. It provides a mathematical way to test whether entanglement is truly non-local. Experiments testing Bell's theorem have consistently supported the quantum mechanical view.