  We examine a situation in which an information-carrying signal is sent from
two sources to a common receiver. The radiation travels through free space in
the presence of noise. The information resides in a relationship between the
two beams. We inquire into whether itis possible, in principle, that the
locations of the transmitters can be concealed from a party who receives the
radiation and decodes the information. Direction finding entails making a set
of measurements on asignal and constructing an analytic continuation of the
time dependent fields from the results. The fact that this process is generally
different in quantum mechanics and in classical electrodynamics is the basis in
this investigation. We develop a model based upon encoding information into a
microscopic, transverse, non-local quantum image (whose dimensions are of the
order of a few wavelengths) and using a detector of a type recently proposed by
Strekalov et al. The optical system, which uses SPDC (Spontaneous Parametric
Down Conversion), functions like a Heisenberg microscope: the transverse
length, which encodes the signal information, is conjugate to the transverse
momentum of the light. In the model, reading the signal information spoils the
directional resolution of the detector, while determining the directions to the
sources spoils the information content. Each beam, when examined in isolation,
is random and indistinguishable from the background noise. We conclude that
quantum communications can, in principle, be made secure against
direction-finding, even from the party receiving the communication.
