Entanglement entropy scaling in solid-state spin arrays via capacitance measurements

TL;DR

This paper demonstrates a method to measure the entanglement entropy scaling in solid-state spin arrays using capacitance measurements, enabling verification of many-body entanglement properties in engineered quantum systems.

Contribution

It introduces a novel measurement protocol using capacitance and replicas to verify entanglement entropy scaling in solid-state spin arrays, bridging theory and experimental realization.

Findings

Entanglement entropy scaling can be verified with minimal replicas and capacitance measurements.

The method is robust against typical device imperfections.

It enables simulation of quantum field theories and bounds on entanglement in solid-state systems.

Abstract

Solid-state spin arrays are being engineered in varied systems, including gated coupled quantum dots and interacting dopants in semiconductor structures. Beyond quantum computation, these arrays are useful integrated analog simulators for many-body models. As entanglement between individual spins is extremely short ranged in these models, one has to measure the entanglement entropy of a block in order to truly verify their many-body entangled nature. Remarkably, the characteristic scaling of entanglement entropy, predicted by conformal field theory, has never been measured. Here we show that with as few as two replicas of a spin array, and capacitive double-dot singlet-triplet measurements on neighboring spin pairs, the above scaling of the entanglement entropy can be verified. This opens up the controlled simulation of quantum field theories, as we exemplify with uniform chains and Kondo-type impurity models, in engineered solid-state systems. Our procedure remains effective even in the presence of typical imperfections of realistic quantum devices and can be used for thermometry, and to bound entanglement and discord in mixed many-body states.