  Quantum tomography is a method to experimentally extract all that is
observable about a quantum mechanical system. We introduce quantum tomography
to collider physics with the illustration of the angular distribution of lepton
pairs. The tomographic method bypasses much of the field-theoretic formalism to
concentrate on what can be observed with experimental data, and how to
characterize the data. We provide a practical, experimentally-driven guide to
model-independent analysis using density matrices at every step. Comparison
with traditional methods of analyzing angular correlations of inclusive
reactions finds many advantages in the tomographic method, which include
manifest Lorentz covariance, direct incorporation of positivity constraints,
exhaustively complete polarization information, and new invariants free from
frame conventions. For example, experimental data can determine the
$entanglement$ $entropy$ of the production process, which is a
model-independent invariant that measures the degree of coherence of the
subprocess. We give reproducible numerical examples and provide a supplemental
standalone computer code that implements the procedure. We also highlight a
property of $complex$ $positivity$ that guarantees in a least-squares type fit
that a local minimum of a $\chi^{2}$ statistic will be a global minimum: There
are no isolated local minima. This property with an automated implementation of
positivity promises to mitigate issues relating to multiple minima and
convention-dependence that have been problematic in previous work on angular
distributions.
