  We present a quantum master equation describing a Bose-Einstein condensate
with particle loss on one lattice site and particle gain on the other lattice
site whose mean-field limit is a non-Hermitian PT-symmetric Gross-Pitaevskii
equation. It is shown that the characteristic properties of PT-symmetric
systems, such as the existence of stationary states and the phase shift of
pulses between two lattice sites, are also found in the many-particle system.
Visualizing the dynamics on a Bloch sphere allows us to compare the complete
dynamics of the master equation with that of the Gross-Pitaevskii equation. We
find that even for a relatively small number of particles the dynamics are in
excellent agreement and the master equation with balanced gain and loss is
indeed an appropriate many-particle description of a PT-symmetric Bose-Einstein
condensate.
