A method is provided for distributing a random list of binary values between first and second parties. The method includes sending photons from the second party into an interferometer at a first beam splitter; performing a first weak measurement on photons as a first pointer result into a first time-ordered list for photons; performing a second weak measurement by the first party on photons that pass through a second beam splitter as being a second pointer result into a second time-ordered list; recording identification for first and second detectors that the photons arrive via a third beam splitter as respective first and second detector registrations for collecting in a third time-ordered list as respective first and second detection lists; determining first and second averages of the respective first and second detection lists; and comparing the averages to verify existence of a non-trivial difference that indicates secure communication status of the element's binary value.