Quantum sensing with critical systems: impact of symmetry, imperfections, and decoherence

TL;DR

This work probes interferometric quantum sensing with critical many-body states, showing that symmetry-informed measurement strategies can harness enhanced quantum Fisher information near quantum phase transitions. It compares critical-state protocols to GHZ and spin-squeezed probes, analyzes robustness to non-unitary deformation and various decoherence channels, and demonstrates that, under favorable conditions, critical states can outperform classical limits and even rival GHZ performance in noisy settings. The study also reveals that non-unitary deformation can, in some scenarios, enhance sensing via decoding procedures and Luttinger-liquid physics, and discusses practical aspects of state preparation with log-depth circuits. Overall, critical-state metrology emerges as a promising route for robust, high-precision sensing in platforms like Rydberg-atom arrays, while highlighting open questions about mixed-state QFI, broader universality classes, and error-mitigation strategies.

Abstract

Entangled many-body states enable high-precision quantum sensing beyond the standard quantum limit. We develop interferometric sensing protocols based on quantum critical wavefunctions and compare their performance with Greenberger-Horne-Zeilinger (GHZ) and spin-squeezed states. Building on the idea of symmetries as a metrological resource, we introduce a symmetry-based algorithm to identify optimal measurement strategies. We illustrate this algorithm both for magnetic systems with internal symmetries and Rydberg-atom arrays with spatial symmetries. We study the robustness of criticality for quantum sensing under non-unitary deformations, symmetry-preserving and symmetry-breaking decoherence, and qubit loss -- identifying regimes where critical systems outperform GHZ states and showing that non-unitary deformation can even enhance sensing precision. Combined with recent results on log-depth preparation of critical wavefunctions, interferometric sensing in this setting appears increasingly promising.

Figures (7)

• Figure 1: Protocol. Given a critical many-body state $\ket{\psi}$, we consider a protocol of quantum sensing in which we first encode the parameter to be estimated, $\theta$, to maximize the quantum Fisher information. An optimal measurement is then performed, yielding outcome statistics that achieve the minimal estimation uncertainty, $\delta\theta$.
• Figure 2: A Hadamard test that measures $\mathrm{Re}\langle \psi_\theta | T | \psi_\theta \rangle$. The orange box represents a controlled-tranlation (C-$T$) gate, which is realized by sequentially applying controlled-swap gates (green boxes) on nearest-neighbor sites. Each controlled-swap gate $\mathrm{C\text{-}SWAP}_{i,i+1}$ is decomposed into three successive Toffoli (controlled-controlled-NOT) gates, $\mathrm{C\text{-}SWAP}_{i,i+1} = \mathrm{C\text{-}CNOT}_{i,i+1}\,\mathrm{C\text{-}CNOT}_{i+1,i}\,\mathrm{C\text{-}CNOT}_{i,i+1}$.
• Figure 3: Quantum Fisher information and optimal measurements. (a) Parity, reflection and translation measurement for the Ising critical ground state at $J/h=\pm 1$. Although the simulations are done for the pure transverse-field Ising model, in the antiferromagnetic case identical scaling behavior arises if a longitudinal field $\sum_j Z_j$ is included, since it comprises an irrelevant perturbation. (b) Quantum Fisher information $F_{Q}$ of different metrological resources as a function of system size $L$. Green triangle: GHZ state and the Heisenberg-limit scaling; Blue circle: Ising critical ground state at $J/h=1$; Red diamond: Ising critical ground state at $J/h=-1$ (only even $L$'s are considered); Dark square: Spin coherent state and the Standard-quantum-limit scaling. The $F_{Q}$'s in (b) are computed at $\theta=0$, though the QFI is independent of $\theta$ in our setup.
• Figure 4: A generalized cluster-state with interchain-reflection symmetry constructed by completing $ZXZ$ terms on all the triangles.
• Figure 5: