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.
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