  We study low energy excitations in the quantum breathing pyrochlore
antiferromagnet Ba$_3$Yb$_2$Zn$_5$O$_{11}$ by combination of inelastic neutron
scattering (INS) and thermodynamical properties measurements. The INS spectra
are quantitatively explained by spin-1/2 single-tetrahedron model having $XXZ$
anisotropy and Dzyaloshinskii-Moriya interaction. This model has a two-fold
degeneracy of the lowest-energy state per tetrahedron and well reproduces the
magnetization curve at 0.5 K and heat capacity above 1.5 K. At lower
temperatures, however, we observe a broad maximum in the heat capacity around
63 mK, demonstrating that a unique quantum ground state is selected due to
extra perturbations with energy scale smaller than the instrumental resolution
of INS.
