BellZustand

BellZustand, commonly referred to as a Bell state, denotes any of the four maximally entangled two-qubit states that form the Bell basis in quantum information. These states are pure and orthonormal, and they provide a convenient complete basis for the joint state space of two qubits.

The four Bell states are:

|Φ+> = (|00> + |11>)/√2

|Φ−> = (|00> − |11>)/√2

|Ψ+> = (|01> + |10>)/√2

|Ψ−> = (|01> − |10>)/√2

Key properties include maximal entanglement, meaning the two qubits cannot be described independently. Each state has reduced density matrices that are maximally mixed (I/2) for each subsystem. The Bell states are interconvertible by local unitary operations, such as Pauli operators, and they form a complete basis for two-qubit states.

Generation methods vary by platform. In photonic systems, Bell states are commonly produced via spontaneous parametric down-conversion followed by appropriate optical elements. In other platforms, such as superconducting qubits or trapped ions, Bell states can be created by applying a Hadamard gate on one qubit followed by a controlled-NOT gate to generate the entangled pair.

Applications of Bell states are central to quantum information science. They enable quantum teleportation, which transmits an unknown quantum state using entanglement and classical communication; superdense coding, which sends two classical bits with one qubit; and entanglement swapping, which extends entanglement through intermediate systems. Bell-state experiments are fundamental in tests of quantum nonlocality and Bell inequality violations, and they underpin many quantum communication protocols.