Lieb-Mattis states for robust entangled differential phase sensing

TL;DR

This paper proposes entangled states for differential phase sensing in quantum sensors that suppress noise and are efficiently preparable, achieving Heisenberg and sub-standard quantum limit sensitivities.

Contribution

It introduces practical entangled states and cavity-mediated protocols that enhance sensitivity while remaining feasible for current quantum sensor technologies.

Findings

States achieve asymptotic sensitivity scaling similar to optimal states.

Preparation time decreases with system size, enabling scalability.

Numerical simulations confirm effectiveness at realistic cavity parameters.

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. This 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 via 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.