Generation and read-out of many-body Bell correlations with a probe qubit

TL;DR

The paper addresses how to generate and certify non-classical correlations, including entanglement depth and many-body Bell correlations, in an $N$-qubit system using a single probe qubit. It shows that a dispersive central-spin coupling reduces to an effective one-axis twisting Hamiltonian $\hat{H}_{\mathrm{coll}} = -\chi \hat{S}_z^2$ with $\chi = g^2/\Delta$, enabling GHZ-type correlations to develop in the joint system. The probe also serves as a readout, where the off-diagonal element $a$ of the probe’s density matrix encodes off-diagonal elements of $\hat{\varrho}_N$; via a phase imprint and a discrete Fourier transform of $p_n(\theta)$, one can recover the $N$-body Bell correlator $\mathcal{E}_{N}^{(q)} = |\varrho_{N/2,-N/2}|^2$ and related metrological figures such as the spin-squeezing parameter $\xi^2$ and the quantum Fisher information $\mathcal{I}_q$. The framework applies to Lipkin–Meshkov–Glick models and related platforms (BECs, trapped ions, superconducting qubits, Rydberg arrays) and offers a scalable, single-qubit readout route for remote tomography-like certification of non-classicality with potential metrological benefits.

Abstract

As demand for quantum technologies increases, so does the need to generate and classify non-classical correlations in complex many-body systems. We introduce a simple and versatile method for creating and certifying entanglement and many-body Bell correlations. This method relies on a single qubit interacting with an $N$-qubit system. We demonstrate that: (i) such pairwise interaction is sufficient to induce many-body quantum correlations, and (ii) the qubit can serve as a probe to extract all information about these correlations. Thus, single-qubit measurements reveal multi-partite entanglement and $N$-body Bell correlations, enabling the rapid and efficient certification of non-classicality in complex systems.

Figures (2)

• Figure 1: A visualization of a single-qubit probe "observing" a system of $N$ qubits.
• Figure 2: (a): Generation of many-body quantum correlations via single-qubit in central-spin model, Eq. \ref{['eq.ham.int']}. Lines present the Bell correlator $\mathcal{Q}_\mu$ as a function of the normalized time for $\mu=8$ qubits (including the probe qubit). The dashed black line denotes the ideal OAT scheme, while the solid blue is for $g=0.05$ and the quickly oscillating green one uses $g=0.1$. For both cases, $\Omega=11$ and $\omega=1$. (b) and (c): probabilities $p_n(\theta)$ for the separable state (b) and the GHZ state (c), shown for $N=64$. The insets show the Fourier transform of $p_0(\theta)$. The emergence of two peaks in the latter case is a signature of Bell correlations.