Multipartite-Entanglement Tomography of a Quantum Simulator

TL;DR

This paper uses multipartite entanglement tomography via quantum Fisher information to characterize phases and critical points in a long-range quantum Ising chain, including effects of finite temperature, offering a practical method for experimental quantum systems.

Contribution

It introduces a novel application of quantum Fisher information to fully characterize phase diagrams and criticality in long-range quantum Ising models, including finite-temperature effects.

Findings

QFI recognizes phases from long-range antiferromagnetic coupling.

QFI locates quantum critical points with and without a mass gap.

Finite temperature affects multipartite entanglement and phase stability.

Abstract

Multipartite entanglement tomography, namely the quantum Fisher information (QFI) calculated with respect to different collective operators, allows to fully characterize the phase diagram of the quantum Ising chain in a transverse field with variable-range coupling. In particular, it recognizes the phase stemming from long-range antiferromagnetic coupling, a capability also shared by the spin squeezing. Furthermore, the QFI locates the quantum critical points, both with vanishing and nonvanishing mass gap. In this case, we also relate the finite-size power-law exponent of the QFI to the critical exponents of the model, finding a signal for the breakdown of conformal invariance in the deep long-range regime. Finally, the effect of a finite temperature on the multipartite entanglement, and ultimately on the phase stability, is considered. In light of the current realizations of the model with trapped ions and of the potential measurability of the QFI, our approach yields a promising strategy to probe long-range physics in controllable quantum systems.