Fundamentals of cryptography

The essence of the Einstein–Podolsky–Rosen experiment analyzed in the preceding chapter is our ability to provide two observers with unpolarized light beams, consisting of sequences of photons, which are coupled in a miraculous way. When both observers choose the same measurement apparatus – a polarizing prism with two detectors in the two output ports, whereby the orientation of the prism is set arbitrarily but identically for both observers – their measurement results are identical. The measurement result, characterized, say, by “0” and “1”, is a genuine random sequence – the quantum mechanical randomness rules unrestricted – from which we can form a sequence of random numbers using the binary number system. The experimental setup thus allows us to deliver simultaneously to the two observers an identical series of random numbers. This would be, by itself, not very exciting. Mathematical algorithms can be used to generate random numbers, for example the digit sequence of the number π, which can be calculated up to an arbitrary length. Even though we cannot be completely sure that such a sequence is absolutely random, such procedures are sufficient for all practical purposes. The essential point of the Einstein–Podolsky–Rosen experiment is that “eavesdroppers” cannot listen to the communication without being noticed by the observers. When eavesdroppers perform an observation on the photons sent, they inevitably destroy the subtle quantum mechanical correlations, and this damage is irreparable.