Diagnosing Quark–Gluon Entanglement Beyond Spatiotemporal Separation: A Sensitivity–Specificity Framework ( By Hema Kasisomayajula)

**Summary / Description** This manuscript examines **quantum entanglement (QE)** beyond traditional **spatiotemporal diagnostics**, addressing regimes where geometric separation between entangled subsystems collapses, such as **confined quark–gluon systems** within hadrons or **high-energy particle collisions**. Standard approaches based on **Bell-type inequalities** and spatial separation are insufficient to uniquely identify entanglement in these dense, ultra-fast environments. We introduce a **correlation-based framework** utilizing **sensitivity and specificity metrics** to classify and detect quantum correlations when spatiotemporal markers are degenerate. We review the **earliest experimental recordings of entanglement**, including the **Freedman–Clauser (1972) experiment** and subsequent **Aspect et al. (1982) demonstrations**, as foundational cases of photon entanglement. At higher energy scales, **ATLAS (2024)** observations of **top quark pair entanglement** highlight the persistence of quantum correlations among partons, while **heavy-ion collision experiments (NA35, NA49)** provide empirical evidence that hadronic outputs encode **underlying quark–gluon correlated behavior**. Despite the lack of unique spatiotemporal signatures for these events, correlations manifest as measurable, **information-theoretic constraints** among dynamical degrees of freedom, offering a pathway to identify **unique entanglement events in dense QCD media**. By drawing a parallel with **Navier–Stokes turbulence**, where local geometric intuition fails but correlations remain measurable, the manuscript proposes that **ubiquitous entanglement** in confined systems can be systematically identified using **statistical and structural diagnostics**. Keywords for discoverability include: **quantum entanglement, quark-gluon plasma, heavy-ion collisions, top quark entanglement, correlation-based diagnostics, sensitivity, specificity, QCD, nonlocal correlations, high-energy physics, confined systems, information-theoretic entanglement, Navier–Stokes analogy, dense matter quantum correlations**. This work provides a **conceptual and methodological framework** for understanding and identifying entanglement in regimes where traditional spacetime-based signatures fail, offering a bridge between **high-energy particle physics, quantum information theory, and statistical correlation diagnostics**.