Measuring a QED cross section via a witness particle

• Published in: arXiv.org 2019-07
• Main Authors: Araujo, Jonas B, Hiller, B, da Paz, I G, Sampaio, Marcos, Costa, H A S
• Format: Article
• Language: English
• Subjects: Cross-sections; Quantum electrodynamics; Scattering; Subsystems
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1907.10466

We consider a QED scattering (\(AB\rightarrow AB\)), in which \(B\) is initially entangled with a third particle (\(C\)) that does not participate directly in the scattering. The effect of the scattering over \(C\)'s final state is evaluated and we note coherence (off-diagonal) terms are created, which lead to non null values for \(\langle \sigma_x\rangle\) and \(\langle \sigma_y\rangle\) that are, in principle, measurable in a Stern-Gerlach apparatus. We chose a particular QED scattering (\(e^+e^-\rightarrow\mu^+\mu^-\)) and found that \(\langle \sigma_x\rangle\) and \(\langle \sigma_y\rangle\) are proportional to the total cross section (\(\sigma_{\text{total}}\)) of the \(AB\) scattering, besides being maximal if \(BC\)'s initial state is taken as a Bell basis. Furthermore, we calculated the initial and final mutual informations \(I_{AC}\) and \(I_{BC}\), and noticed an increase (decrease) in \(I_{AC}\) (\(I_{BC}\)), which indicates that, after \(AB\) interact, the total amount of correlations (quantum \(+\) classical) are distributed among the \(3\) subsystems.