  We review, correct, and develop an algorithm which determines arbitrary
Quantum Bounds, based on the seminal work of Tsirelson [Lett. Math. Phys. 4, 93
(1980)]. The potential of this algorithm is demonstrated by deriving both new
number-valued Quantum Bounds, as well as identifying a new class of
function-valued Quantum Bounds. Those results facilitate an 8-dimensional
Volume Analysis of Quantum Mechanics which extends the work of Cabello [PRA 72
(2005)]. We contrast the Quantum Volume defined be these new bounds to that of
Macroscopic Locality, defined by the inequalities corresponding to the first
level of the hierarchy of Navascues et al [NJP 10 (2008)], proving our
function-valued Quantum Bounds to be more complete.
