## The More You Know: Bell States/EPR Pairs

Bell States (named after John S. Bell) or EPR pairs (after Einsetin, Podolski and Rosen Paradox) are the maximally entangled quantum states of a two qubit system (i.e. a quantum mechanical system composed of two interacting two-level subsystems).

In the computational basis $\{|00\rangle,|01\rangle,|10\rangle,|11\rangle\}$ the four maximally entangled Bell states are expressed as

$|\Phi^\pm\rangle=\frac{|00\rangle\pm|11\rangle}{\sqrt{2}}$,

$|\Psi^\pm\rangle=\frac{|00\rangle\pm|11\rangle}{\sqrt{2}}$.

To understand the correlations present in these states consider the Bell state $|\Phi^+\rangle=\frac{|00\rangle+|11\rangle}{\sqrt{2}}$. If a measurement is performed on the first qubit the result may be 0 or 1, after which the two qubit state collapses to $|00\rangle$ or $|11\rangle$ respectively. Then, a measurement on the second qubit must result in 0 or 1, yielding the same result as the measurement on the first one. That is, the outcomes of the measurements are correlated.

John Bell proved that the correlations present in EPR pairs cannot be accounted for by any classical theory. See this article for more.