Bell state

A Bell state is one of four maximally entangled states of two qubits. Together they form an orthonormal basis and exhibit correlations that cannot be explained by local hidden-variable theories.

Qubit: A qubit is a two-level quantum system whose state can be a superposition of two basis states. Each Bell state describes a pair of these two-level quantum systems.
Bell basis: The Bell basis is the orthonormal basis of four maximally entangled states for a pair of qubits. It treats the four Bell states as a complete basis for two-qubit measurements and protocols.
Quantum teleportation: Quantum teleportation transfers an unknown quantum state using shared entanglement and classical communication. A shared Bell pair supplies the entanglement resource consumed by the protocol.
Product state: A product state is a composite quantum state expressible as a tensor product of states for its separate subsystems. Unlike a Bell state, it has no entanglement between its two qubits.
Quantum superposition: Quantum superposition is the linear combination of possible states that defines a quantum system’s state before measurement. Bell states combine two-qubit basis states with precise relative phases.
CNOT gate: The controlled-NOT gate flips a target qubit when its control qubit is one. Combined with a Hadamard gate, it can prepare Bell states from computational-basis inputs.
Superdense coding: Superdense coding transmits two classical bits by sending one qubit, using a previously shared entangled pair. Local operations encode messages as distinct Bell states for joint decoding.
Separable state: A separable state is a quantum state expressible as a mixture of product states across a specified division of a system. Bell states are entangled pure states, not mixtures of uncorrelated subsystem states.
Quantum entanglement: Quantum entanglement is a relationship in which a composite quantum state cannot be separated into independent states of its parts. It is the defining property that distinguishes Bell states from product states.
Hadamard gate: The Hadamard gate maps computational-basis states to equal superpositions and reverses that transformation. It creates the superposition that a CNOT gate turns into a Bell state.

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