Quantum tomography for collider physics: Illustrations with lepton pair production

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.