Abstract
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. 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. 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.
Highlights
Tomography builds up higher-dimensional objects from lower-dimensional projections
Quantum tomography [1] is a strategy to reconstruct all that can be observed about a quantum physical system
After becoming a focal point of quantum computing, quantum tomography has recently been applied in a variety of domains [2,3,4,5,6,7,8,9]
Summary
Tomography builds up higher-dimensional objects from lower-dimensional projections. Quantum tomography [1] is a strategy to reconstruct all that can be observed about a quantum physical system. The method of quantum tomography uses a known “probe” to explore an unknown system. Data is related directly to matrix elements, with minimal model dependence and optimal efficiency. Collider physics is conventionally set up in a framework of unobservable and model-dependent scattering amplitudes. In quantum tomography these unobservable features are skipped to deal directly with observables. We illustrate the advantages of quantum tomography with inclusive lepton-pair production. It is a relatively mature subject chosen for its pedagogical convenience. Our practical guide to analyzing experimental data uses density matrices at each step and circumvents the more elaborate traditional theoretical formalism. We give a step-by-step guide where density matrices stand as definite arrays of numbers, bypassing unnecessary formalism
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