Generation of many-body Bell correlations with short-range interactions in analog and digital quantum simulators

Abstract

The dynamical generation of quantum resources, such as many-body entanglement or Bell correlations, can be achieved via one-axis twisting (OAT) dynamics, which require all-to-all couplings. However, current digital and analog quantum simulation platforms natively provide short-range or power-law couplings that decay too quickly for this purpose. We demonstrate that two spin-$\tfrac12$ chain models -- a staggered nearest-neighbor XXX chain and a long-range XXZ chain -- develop an effective OAT nonlinearity when projected onto the symmetric sector. We show that these dynamics generate metrologically useful spin-squeezed states and Greenberger-Horne-Zeilinger coherences that ensure violation of many-body Bell inequalities. We confirm the accuracy of this mapping by comparing it to the exact dynamics and demonstrate that the generated correlations can be read out using a single probe qubit. The resulting dynamics can be simulated with analog and digital quantum simulators

Figures (7)

• Figure 1: Time evolution of the Bell correlator $\mathcal{Q}(t)$ for $N=10$ spins and $h_z=0.15$ in the staggered XXX chain. The solid line corresponds to the collective OAT results. The dashed line corresponds to the exact analog evolution under the XXX Hamiltonian obtained from full diagonalization. The dotted line shows the Trotterized dynamics generated by the digital quantum circuit. The three curves coincide when time is rescaled by the effective OAT coupling. For weak staggered fields, all implementations agree and display a pronounced peak in $\mathcal{Q}(t)$, signaling the creation of GHZ-like correlations via the effective $\hat{S}_z^2$ twisting.
• Figure 2: Probe-qubit certification of the many-body Bell correlator for the staggered XXX model, Eq. \ref{['eq:H_staggered_XXX']}, with $N = 10$, $h_z = 0.1$, and periodic boundary conditions. Left panel: probability $p_{m=0}(\theta)$ as a function of the imprinted phase $\theta$, shown for states with Bell correlators $\mathcal{Q} = 1, 6, 8$. Right panel: squared Fourier amplitudes $|F_k[p_0]|^2$ as a function of the harmonic index $k$. In agreement with the parity constraint of the Wigner $d$-matrix, only even harmonics contribute. The GHZ-sensitive mode at $k=N$ grows systematically with $\mathcal{Q}$.
• Figure 3: Bell correlations in the long-range XXZ model $\hat{H}_{\mathrm{XXZ}}$ of Eq. \ref{['eq:H_XXZ_main']} with periodic boundary conditions. Left: maximal Bell correlator $\tilde{\mathcal{Q}}$ as a function of the exponent $\gamma$ and anisotropy $\delta$. Right: time traces $\mathcal{Q}(t)$ for the selected pairs $(\gamma,\delta)$ marked (a)--(d) in the phase diagram. Large $\tilde{\mathcal{Q}}$ indicates regimes where the SW mapping to OAT with coupling $\chi$ from Eq. \ref{['eq:H_OAT_XXZ']} is accurate.
• Figure 4: Spin squeezing from microscopic spin chains (solid lines) compared with the effective OAT prediction (non-solid lines). (a) Staggered XXX ($N=10$): $\xi_R^2(t)$ for several field strengths $h$. (b) Long-range XXZ ($N=10$): $\xi_R^2(t)$ for representative pairs $(\delta,\gamma)$. (c) Staggered XXX: optimal squeezing $\min_t\xi_R^2$ vs. $h$ for different $N$ (circles: chain; squares: OAT). (d) Long-range XXZ ($N=8$): $\delta$-$\gamma$ phase diagram of $\min_t\xi_R^2$; the black contour marks $\xi_R^2=1$.
• Figure 5: One-magnon dispersion relation: analytical (solid lines) vs. exact diagonalization in the single-flip basis (circles), $N=30$. (a) Nearest-neighbour isotropic Heisenberg with $h_z=0$. (b) Long-range XXZ, for representative $(\delta,\gamma)$ pairs spanning isotropic long-range to strongly anisotropic short-range regimes.