  Multiparty quantum communication provides delightful applications including
quantum cryptographic communication and quantum secret sharing.
Measurement-Device-Independent (MDI) quantum communication based on the
Greenberg-Horne-Zeilinger (GHZ) state measurement provides a practical way to
implement multiparty quantum communication. With the standard spatially
localized GHZ state measurement, however, information can be imbalanced among
the communication parties that can cause significant problems in multiparty
cryptographic communication. Here, we propose an equitable multiparty quantum
communication where information balance among the communication parties is
achieved without a trusted third party. Our scheme is based on the GHZ state
measurement which is not spatially localized but implemented in a way that all
the distant communication parties symmetrically participate. We also verify the
feasibility of our scheme by presenting the proof-of-principle experimental
demonstration of informationally balanced three-party quantum communication
using weak coherent pulses.
