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arXiv:1707.01638 · The European Physical Journal C

Quantum tomography for collider physics: illustrations with lepton-pair production

John C. Martens, John P. Ralston, J. D. Tapia Takaki

Published Dec 30, 2017• 28 citations

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.

DOI: 10.1140/epjc/s10052-017-5455-8

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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

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Quantum detection of CP violation in the

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system: tomography

We develop a quantum-tomographic framework for determining whether possible CP-odd effects in

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events originate in production, in decay, or in both. In the narrow-width approximation, the process

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factorises into a production density matrix and top and antitop decay density matrices. We extend the standard tomography procedure to a general anomalous

Wtb

vertex and derive the corresponding angular distributions. Polar-angle distributions retain their usual tomographic form, up to modifications of the spin-analysing powers, and can therefore be used to reconstruct the production density matrix and test its CP properties. By contrast, dedicated azimuthal observables involving the

b

--lepton decay planes contain characteristic sine modulations that provide linear probes of possible new CP-violating interactions in the decay vertex. Combining the two classes of observables gives a systematic strategy for separating sources of CP violation in production and in decay. We illustrate the resulting angular signatures for representative

t\bar t

production scenarios at hadron and lepton colliders.

Quantum tomography has become an indispensable tool in order to compute the density matrix ρ of quantum systems in physics. Recently, it has further gained importance as a basic step to test entanglement and violation of Bell inequalities in high-energy particle physics. In this work, we present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process. In particular, we perform an expansion of ρ over the irreducible tensor operators { T M L } and compute the corresponding coefficients uniquely by averaging, under properly chosen Wigner D-matrices weights, the angular distribution data of the final particles. Besides, we provide the explicit angular dependence of a novel generalization of the production matrix Γ and of the normalized differential cross section of the scattering. Finally, we rederive all our previous results from a quantum-information perspective using the Weyl-Wigner-Moyal formalism and we obtain, in addition, simple analytical expressions for the Wigner P and Q symbols. Published by the American Physical Society 2024

Abstract In quantum information theory, the evolution of an open quantum system—a unitary evolution followed by a measurement—is described by a quantum channel or, more generally, a quantum instrument. In this work, we formulate spin and flavour measurements in collider experiments as quantum instruments. We demonstrate that the Choi matrix, which completely determines input-output transitions, can be both theoretically computed from a given model and experimentally reconstructed from a set of final state measurements (quantum state tomography) using varied input states. The experimental reconstruction of the Choi matrix, known as quantum process tomography, offers a powerful new approach for probing potential extensions of the Standard Model, which predict different input-output transitions. In addition, the methodology constitutes a new foundational test of quantum mechanics itself. As an example, we outline the quantum process tomography approach applied to the e + e − → t t ¯ process at a polarised lepton collider.

Entanglement, a fundamental phenomenon of quantum theory, has recently been observed in processes in high-energy physics. This opens new avenues for probing quantum effects in relativistic regimes, but also poses conceptual and technical challenges. We develop a general framework based on shadow tomography techniques for characterising spin-spin correlations in collider experiments. This improves the analysis of spin-spin entanglement, where relativistic motion couples spin and momentum and the momenta of the investigated particles are not under experimental control. As a proof of concept we illustrate the application of our formalism to top quark pair production at the Large Hadron Collider at CERN. The framework, however, is general and flexible and can be readily applied to more complex final states and systems with more particles.

Abstract Quantum tomography, as a tool to probe foundational aspects of quantum mechanics, relies on extracting spin information from angular distributions. This is inherently a leading-order technique, ill-defined when higher-order corrections are significant. For those cases, we propose to treat higher-order corrections as a background, to be modeled and subtracted from data in the same way as other backgrounds are. We illustrate this procedure for Higgs decays

H \rightarrow ZZ \rightarrow e^+ e^- \mu ^+ \mu ^-

H → Z Z → e + e - μ + μ - , which is of high interest for upcoming qutrit entanglement tests at the Large Hadron Collider.