It is demonstrated that the recently developed technique of delocalized single photon addition may generate discorrelation, a new joint statistical property of multimode quantum light states, whereby the number of photons in each mode can take any value individually, but two modes together never exhibit the same. By coherently adding a single photon to two identical coherent states of light in different temporal modes, the first experimental observation of discorrelation is provided. The capability of manipulating this statistical property has applications in scenarios involving the secure distribution of information among untrusted parties, like in the so‐called “mental poker” games.