Probing holographic conformal field theories

Abstract

We introduce an operational, boundary-first framework that embeds relativistic quantum-information protocols into anti-de Sitter/Conformal Field Theory (AdS/CFT) by coupling an Unruh--DeWitt detector directly to a local scalar primary operator of a holographic CFT. Using the universal CFT Wightman function, we compute the detector's reduced density operator perturbatively, retaining both excitation probabilities and coherences. As a concrete resource-theoretic application, we implement magic resource (mana) harvesting with a qutrit probe. For a CFT dual to global AdS, we show that the harvested mana sharply distinguishes the two admissible scalar quantizations in the Breitenlohner--Freedman window, with the standard quantization yielding systematically larger mana than the alternate one. Our results provide a viable way of testing holography principle through quantum information resource.

Figures (2)

• Figure 1: Schematic holographic setup. A probe scalar field $\Phi$ in global AdS$_{d+1}$ is dual to a scalar primary operator $\hat{\mathcal{O}}$ on the conformal boundary $\mathbb{R}_\tau\times S^{d-1}_R$. Detectors may be coupled either to $\Phi$ in the bulk or to $\hat{\mathcal{O}}$ on the boundary; we focus on a static boundary detector coupled to $\hat{\mathcal{O}}$.
• Figure 2: Mana $M$ versus detector energy gap $\Omega$ for a static qutrit UDW detector in a $d=3$ CFT on $\mathbb{R}_\tau\times S^2_R$ for $R=1$, $\sigma=1, \lambda=1$, comparing the two admissible holographic quantizations $\Delta=\Delta_\pm$ of the dual scalar sector. For reference we also show the corresponding bulk AdS curves reproduced from Yang:2025zrl, clarifying that a local bulk detector approaching the boundary does not generically reproduce the local boundary-detector protocol.