The compressibility factor of the quantum hard-sphere fluid within the region (rho(N)(*)less than or equal to0.8,lambda(B)(*)less than or equal to0.9) is computed by following four distinct routes involving the three pair radial correlation functions that are significant in the path-integral context, namely, instantaneous, pair linear response, and centroids. These functions are calculated with path-integral Monte Carlo simulations involving the Cao-Berne propagator. The first route to the equation of state is the instantaneous standard one, i.e., the usual volume derivative of the partition function expressed in terms of the instantaneous pair radial correlations. The other three routes stem from the extended compressibility theorem, which associates the isothermal compressibility with the three pair radial structures mentioned above and involves the solving of appropriate Ornstein-Zernike equations. An analysis of the error bars in the quantities computed is reported, and it is proven the usefulness of the centroid pair correlations to fix quantum equations of state. Also, the regions where the fluid-solid changes of phase should take place are identified with the use of indicators sensitive to order in the sample. The consistency of the current results is assessed and comparison with data available in the literature is made wherever possible. (C) 2004 American Institute of Physics.