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arXiv:2409.15249 · Materials Today Quantum

Tutorial: Extracting entanglement signatures from neutron spectroscopy

Allen O. Scheie, Pontus Laurell, Wolfgang Simeth, Elbio R. Dagotto, D. M. Tennant

Published Dec 16, 2024• 9 citations
arXivHTMLPDF

Abstract

This tutorial is a pedagogical introduction to recent methods of computing quantum spin entanglement witnesses from spectroscopy, with a special focus on neutron scattering on quantum spin systems. We offer a brief introduction to the concepts and equations, define a data analysis protocol, and discuss the interpretation of three entanglement witnesses: one-tangle, two-tangle, and Quantum Fisher Information . We also discuss practical experimental considerations, and give three examples of extracting entanglement witnesses from experimental data: Copper Nitrate, KCuF 3 , and NiPS 3 .

DOI
10.1016/j.mtquan.2024.100020

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This tutorial is a pedagogical introduction to recent methods of computing quantum spin entanglement witnesses from spectroscopy, with a special focus on neutron scattering on quantum spin systems. We offer a brief introduction to the concepts and equations, define a data analysis protocol, and discuss the interpretation of three entanglement witnesses: one-tangle, two-tangle, and Quantum Fisher Information . We also discuss practical experimental considerations, and give three examples of extracting entanglement witnesses from experimental data: Copper Nitrate, KCuF 3 , and NiPS 3 .
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The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.
Multipartite entanglement was thought to be intrinsically difficult to measure in solids, but recent work has established connections between multipartite entanglement, dynamic susceptibilities, and neutron scattering data, via the quantum Fisher information. This work focuses on the paradigmatic spin-half chain and shows that there are further simplifications: even static structure factors contain quantitative information about multipartite entanglement at low temperatures. Theory, numerics, and experiment then suggest that a high degree of multipartite entanglement is observable in Heisenberg chain compounds, including KCuF3{}_{3}3​.
Entanglement, a defining property of quantum mechanics in which two physical subsystems cannot be seen as independent entities, challenges our everyday experience and classical intuition. However, only such strong quantum correlations enable quantum technologies, including quantum computing or communication, while revealing the limits of our classical worldview by violating local realism. Given its importance in modern quantum science, we present this tutorial addressing the questions: What is entanglement, how does it differ from classical correlations, and how can it be experimentally verified? Using celebrated examples, such as Schrödinger's cat, we highlight the distinction between classical and quantum correlations and illustrate the definition of entangled and separable states. We review entanglement criteria by discussing Heisenberg-type uncertainty relations for continuous variables and the CHSH inequality for discrete systems. Focusing on concepts of quantum correlations and operational entanglement witnesses, we provide accessible tools and illustrative examples aimed at demystifying entanglement for a broad readership.
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