  A continuous variable (CV), measurement device independent (MDI) quantum key
distribution (QKD) protocol is analyzed, enabling three parties to connect for
quantum conferencing. We utilise a generalised Bell detection at an untrusted
relay and a postselection procedure, in which distant parties reconcile on the
signs of the displacements of the quadratures of their prepared coherent
states. We derive the rate of the protocol under a collective pure-loss attack,
demonstrating improved rate-distance performance compared to the equivalent
non-post-selected protocol. In the symmetric configuration in which all the
parties lie the same distance from the relay, we find a positive key rate over
6 km. Such postselection techniques can be used to improve the rate of
multi-party quantum conferencing protocols at longer distances at the cost of
reduced performance at shorter distances.
