Bell state
The Bell states are a concept in quantum information science and represent the simplest examples of entanglement. They are named after John S. Bell because they are the subject of his famous Bell inequality. An EPR pair is a pair of qubits (or quantum bits) that are in a Bell state together, that is, entangled with each other. Unlike classical phenomena such as the nuclear, electromagnetic, and gravitational fields, entanglement is invariant under distance of separation and is not subject to relativistic limitations such as the speed of light (though the no-communication theorem prevents this behaviour being used to transmit information faster than light, which would violate causality).
The Bell states are four specific maximally entangled quantum states of two qubits.
The degree to which a state in a quantum system consisting of two "particles" is entangled is measured by the Von Neumann entropy of either of the two reduced density operators of the state. The Von Neumann entropy of a pure state is zero—also for the bell states, which are specific pure states. But the 2x2 density matrix corresponding to the Bell states can be formed as usual, and the von Neumann entropy of this density operator of the Bell states is positive and maximal, if the matrix does not degenerate to a projector.
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