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Lieb-Mattis States for Robust Entangled Differential Phase Sensing

Raphael Kaubruegger1, Diego Fallas Padilla1, Athreya Shankar2,3, Christoph Hotter4, Sean R. Muleady5,6, Jacob Bringewatt7, Youcef Baamara1, Erfan Abbasgholinejad5,6, Alexey V. Gorshkov5,6 et al.

Klaus Mølmer4, James K. Thompson1, and Ana Maria Rey1,8

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Phys. Rev. X 16, 021052 – Published 9 June, 2026

DOI: https://doi.org/10.1103/ksyh-mb4s

Abstract

We explore a two-node, entanglement-enhanced sensor network for differential phase sensing that exploits decoherence-free subspaces to suppress common-mode noise, a primary limitation of many state-of-the-art quantum sensors. We identify a class of entangled states that, while not strictly optimal, achieve the same asymptotic sensitivity scaling as optimal states and can be prepared efficiently from initially unentangled atomic ensembles. Importantly, the preparation time decreases with increasing system size, which makes the states compatible with realistic noise processes in present-day quantum sensors that operate with large particle numbers but lack full error correction. We illustrate these ideas using two cavity-mediated preparation protocols: (i) coherent, unitary entanglement generation analogous to bosonic two-mode squeezing, yielding Heisenberg scaling, and (ii) dissipative preparation through collective emission into a shared cavity mode, providing a square-root improvement beyond the standard quantum limit. Numerical simulations show that both approaches remain effective at experimentally realistic cavity cooperativities, establishing a practical path toward scalable, quantum-enhanced differential phase sensing.

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Popular Summary

The performance of state-of-the-art quantum sensors is often constrained by common-mode noise, including fluctuations of ambient magnetic fields and the finite coherence time of the electromagnetic fields used for their manipulation. We address this limitation by proposing a two-node quantum-sensor network that operates in a decoherence-free subspace using entangled Lieb-Mattis states. We show that these states achieve optimal asymptotic sensitivity scaling and can be prepared efficiently via coherent cavity-mediated protocols. In addition, we show that collective cavity-mediated dissipation can generate mixed states with Lieb-Mattis-type entanglement that retain a metrological advantage. The required preparation time decreases with system size, rendering these states particularly compatible with realistic noise processes in sensors lacking full error correction. Our results thus establish a practical and robust path toward scalable quantum-enhanced differential phase sensing in precision metrology platforms such as optical clocks and atomic interferometers.

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Phys. Rev. X 16, 021052– Published 9 June, 2026
  • Received 23 June 2025
  • Accepted 16 April 2026
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