  We introduce a ternary quantum key distribution (QKD) protocol and asymptotic
security proof based on three coherent states and homodyne detection. Previous
work had considered the binary case of two coherent states and here we
nontrivially extend this to three. Our motivation is to leverage the practical
benefits of both discrete and continuous (Gaussian) encoding schemes creating a
best-of-both-worlds approach; namely, the postprocessing of discrete encodings
and the hardware benefits of continuous ones. We present a thorough and
detailed security proof in the limit of infinite signal states which allows us
to lower bound the secret key rate. We calculate this is in the context of
collective eavesdropping attacks and reverse reconciliation postprocessing.
Finally, we compare the ternary coherent state protocol to other well-known QKD
schemes (and fundamental repeaterless limits) in terms of secret key rates and
loss.
