The Einstein-Podolsky-Rosen paradox: from concepts to applications

This Colloquium examines the field of the EPR Gedankenexperiment, from the original paper of Einstein, Podolsky and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. We analyze the relationship with entanglement and Bell's theorem, and summarize the progress to date towards experimental confirmation of the EPR paradox, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fibre quantum soliton experiments. We discuss current proposals for extending EPR experiments to massive-particle systems, including spin-squeezing, atomic position entangle- ment, and quadrature entanglement in ultra-cold atoms. Finally, we examine applications of this technology to quantum key distribution, quantum teleportation and entanglement-swapping.