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We investigate ballistic transport and quantum interference in a nanoscale quantum wire loop fab-ricated as a GaAs/AlGaAs field-effect heterostructure. Four-terminal measurements of current and voltage characteristics as a function of top gate voltages show negative bend resistance as a clear signature of ballistic transport. In perpendicular magnetic fields phase-coherent transport leads to Aharonov-Bohm (AB) conductance oscillations which show equal amplitudes in the local and the non-local measurement at a temperature of 1.5 K and above. We attribute this novel observation to the symmetry of the orthogonal cross junctions connecting the four quantum wire leads with the asymmetric quantum wire ring., Comment: 3 pages, 4 figures