  We report detailed dc and ac magnetic susceptibilities, specific heat, and
thermal conductivity measurements on the frustrated magnet ZnCr$_2$Se$_4$. At
low temperatures, with increasing magnetic field, this spinel material goes
through a series of spin state transitions from the helix spin state to the
spiral spin state and then to the fully polarized state. Our results indicate a
direct quantum phase transition from the spiral spin state to the fully
polarized state. As the system approaches the quantum criticality, we find
strong quantum fluctuations of the spins with the behaviors such as an
unconventional $T^2$-dependent specific heat and temperature independent mean
free path for the thermal transport. We complete the full phase diagram of
ZnCr$_2$Se$_4$ under the external magnetic field and propose the possibility of
frustrated quantum criticality with extended densities of critical modes to
account for the unusual low-energy excitations in the vicinity of the
criticality. Our results reveal that ZnCr$_2$Se$_4$ is a rare example of 3D
magnet exhibiting a field-driven quantum criticality with unconventional
properties.
