  We analyse a central broadcast continuous variable quantum key distribution
protocol in which a beam produced by a thermal source is used to create a
secret key between two parties, Alice and Bob. A beamsplitter splits the
initial beam into a pair of output beams, which are sent to Alice and Bob, with
Eve intercepting Bob's beam. We investigate the protocol in detail, using
analytic methods as well as numerically through Monte Carlo simulations. In a
lossless system, we find that a lower bound on the key rate remains positive in
the protocol, provided Bob receives a nonzero proportion of the beam initially
sent to him. This suggests that the thermal state protocol could be used
experimentally to produce secure keys.
