  We have examined superfluid properties of $^4$He confined to a nano-porous
Gelsil glass that has nanopores 2.5 nm in diameter. The pressure-temperature
phase diagram was determined by torsional oscillator, heat capacity and
pressure studies. The superfluid transition temperature $T_{\mathrm c}$
approaches zero at 3.4 MPa, indicating a novel "quantum" superfluid transition.
By heat capacity measurements, the nonsuperfluid phase adjacent to the
superfluid and solid phases is identified to be a nanometer-scale, localized
Bose condensation state, in which global phase coherence is destroyed. At high
pressures, the superfluid density has a $T$-linear term, and $T_{\mathrm c}$ is
proportional to the zero-temperature superfluid density. These results strongly
suggest that phase fluctuations in the superfluid order parameter play a
dominant role on the phase diagram and superfluid properties.
