  In a three-particle extension of Wheeler's delayed choice gedanken
experiment, the quantum statistics of two particles is undetermined until a
third particle is measured. As a function of the measurement result, the
particles behave either as bosons or as fermions. The particles are
distinguishable if no measurement is performed at all or when the measurement
is performed in a rotated basis. The scheme is based on
Greenberger-Horne-Zeilinger quantum correlations. It can be interpreted more
generally as the encryption of maximally entangled states in a larger quantum
superposition. The local quantum information is scrambled but can be decoded by
the measurement result of a control particle. This can be extended to multiple
particles and allows to develop quantum information protocols whose successful
implementation depends on the collaboration of all parties.
