Experimental characterization of the hierarchy of quantum correlations in top quark pairs

TL;DR

The paper analyzes quantum correlations in top-quark pairs produced at the LHC by interpreting CMS’s doubly differential measurements of the ttbar spin density matrix through quantum information observables. It computes discord $D_t$, steering marker $T$, Bell marker $B$, and magic $M_2$ within both the helicity and beam bases, illustrating the hierarchy of quantum correlations in a high-energy system. The results show discord with >5σ significance across several phase-space bins, first evidence for steering (>3σ), no observed Bell correlations in the probed region, and substantial magic (>5σ) consistent with SM predictions. This work bridges quantum information concepts and collider data, offering a new framework to probe fundamental QM properties and potential Beyond-Standard-Model physics as more data become available.

Abstract

Recent results from the Large Hadron Collider have demonstrated quantum entanglement of top quark-antiquark pairs using the spin degree of freedom. Based on the doubly differential measurement of the spin density matrix of the top quark and antiquark performed by the CMS collaboration in the helicity and beam bases, we evaluate a set of quantum observables, including discord, steering, Bell correlation, and magic. These observables allow for a quantitative characterization of the quantum correlations present in a top quark--antiquark system, thus enabling an interpretation of collider data in terms of quantum states and their properties. Discord is observed to be greater than zero with a significance of more than 5 standard deviations ($σ$). Evidence for steering is found with a significance of more than 3$σ$. This is the first evidence for steering, and the first observation of discord in a high-energy system. No Bell correlation is observed within the currently probed phase space, in agreement with the theoretical prediction. These results experimentally corroborate the full hierarchy of quantum correlations in top quarks with discord being the most basic form of quantum correlation, followed by entanglement, steering and Bell correlation. The significance of nonzero magic, which is a complementary observable to the quantum-correlation hierarchy, is found to exceed 5$σ$ in several regions of phase space.

Figures (4)

• Figure 1: Results for quantum discord $\mathcal{D}_{\text{t}}$ (upper row), steering marker $\mathcal{T}$ (middle row), and Bell correlation marker $\mathcal{B}$ (bottom row) in bins of $m(\text{t} \bar{\text{t}}\xspace)$vs.$\lvert \cos(\theta\xspace)\xspace \rvert$ in the helicity (left) and beam (right) bases. The measurements (points) are shown with the total uncertainty and compared to the predictions of powheg+pythia. Horizontal dashed lines indicate the threshold values: 2$\pi$ for $\mathcal{T}$, one for $\mathcal{B}$. The threshold value for $\mathcal{D}_{\text{t}}$ is zero.
• Figure 2: Quantum magic $\tilde{\mathcal{M}}_\mathrm{2}$ in the helicity (left) and beam (right) bases in bins of $m(\text{t} \bar{\text{t}}\xspace)$vs.$\lvert \cos(\theta\xspace)\xspace \rvert$. The measurements (points) are shown with the total uncertainty and compared to the predictions of powheg+pythia. The threshold value for $\tilde{\mathcal{M}}_\mathrm{2}$ is zero.
• Figure 3: Significance in units of $\sigma$ of the discord, entanglement, steering and Bell correlation markers exceeding the threshold values.
• Figure 4: Results of $\mathcal{D}_{\bar{\text{t}}}$ (upper row) and $\mathcal{D}_{\text{t}}\xspace-\mathcal{D}_{\bar{\text{t}}}\xspace$ (bottom row) in bins of $m(\text{t} \bar{\text{t}}\xspace)$vs.$\lvert \cos(\theta\xspace)\xspace \rvert$ in the helicity (left) and beam (right) basis. The measurements (points) are shown with the total uncertainty and compared to the predictions of powheg+pythia. The threshold value for $\mathcal{D}_{\bar{\text{t}}}$ is zero.