Observation of Criticality-Enhanced Quantum Sensing in Nonunitary Quantum Walks

Quantum physics enables parameter estimation with precisions beyond the capability of classical sensors. Quantum criticality is a key resource for this quantum-enhanced sensing, but experimental realization has been challenging due to the complexity of ground-state preparation and the long time required to reach the steady state near criticality. Here, we experimentally demonstrate critical enhancement in a non-Hermitian topological system using a photonic quantum walk setup. Our system supports two distinct phase transitions at which enhanced sensitivity is observed even at transient times for which the Bayesian inference shows excellent estimation and precision. It is a direct demonstration of criticality-enhanced scaling laws with non-unitary dynamics.

💡 Research Summary

Quantum sensing aims to exploit quantum resources to achieve parameter‑estimation precision beyond classical limits. While quantum criticality has been identified as a powerful resource for such enhancement, practical implementations have been hampered by two major obstacles: (i) the need to prepare ground or steady states near a phase transition, which suffers from critical slowing down, and (ii) the difficulty of engineering the specific non‑Hermitian gap structures (point‑gap or line‑gap) that underpin topological phase transitions in open systems. In this work, Xiao et al. present a comprehensive experimental demonstration that overcomes both challenges by using a discrete‑time photonic quantum walk (QW) platform with engineered loss to realize a non‑Hermitian (NH) topological Hamiltonian.

The authors construct a one‑dimensional lattice of size N = 2n + 1, where the internal “coin” degree of freedom is encoded in photon polarization (horizontal H and vertical V). The QW evolution operator U = e^{‑iH_eff} consists of site‑dependent coin rotations R_θ, a shift S that moves the walker left or right depending on its polarization, and a non‑unitary loss operator Γ implemented by a partially polarizing beam splitter (PPBS) that attenuates the V component. By choosing different rotation angles θ_L1, θ_L2 on the left domain and θ_R1, θ_R2 on the right domain, a domain wall is created that supports two distinct topological phase transitions:

1. Point‑gap closing – the bulk spectrum forms a loop in the complex energy plane; at the critical point the loop collapses, eliminating the non‑Hermitian skin effect. The condition for closure under periodic (closed) boundary conditions is θ_L1 + θ_L2 = π.

2. Line‑gap closing – a reference line separates two spectral islands; closing occurs when the islands merge, leading to the disappearance of a symmetry‑protected edge state.

In Hermitian systems, the Fisher information diverges at such critical points, and similar behavior is expected for NH systems. The authors analytically compute the quantum Fisher information (QFI) for two probe choices: (i) the steady state (the eigenstate with the largest imaginary eigenvalue) and (ii) a transient state |Ψ_N⟩ obtained after T = (N − 1)/2 steps, i.e., the minimal time required for the walker to explore the entire lattice. While the steady‑state QFI exhibits the ideal quadratic scaling F_Q ∝ N² at the critical point, reaching this state experimentally would require many additional steps and multiple reflections from the boundaries, which is impractical.

Remarkably, the transient probe already displays a pronounced critical enhancement. Near the point‑gap closure, the QFI of |Ψ_N⟩ grows with system size as F_Q ∝ N^{1.27}, and for the line‑gap closure the exponent is ≈ 1.0, both clearly super‑linear. Away from criticality the QFI becomes size‑independent or sub‑linear (exponents ≈ 0.8–0.9). These theoretical predictions are corroborated by detailed numerical simulations of the full non‑unitary dynamics.

The experimental implementation uses a pulsed laser attenuated to the single‑photon level. Polarization preparation, coin rotations, and shift operations are realized with a sequence of half‑wave plates (HWPs), birefringent beam displacers (BDs), and the PPBS. After the walk, photons are detected at each lattice site by avalanche photodiodes (APDs), providing the normalized position probabilities p_j. From these probabilities the authors compute the classical Fisher information (CFI) for a position measurement and perform Bayesian inference to estimate the unknown rotation angle θ.

Experimental results for point‑gap closing (θ_L1 = θ_R2 = 0.9π, varying θ_L2 = θ_R1) show a clear CFI peak at θ ≈ 0.11π, close to the theoretical critical value 0.10π. The peak CFI scales with N as F_C^{max} ∝ N^{1.2–2.7}, confirming super‑linear enhancement. For line‑gap closing (θ_L1 = θ_R2 = 0.05π, varying θ_L2 = θ_R1) a CFI maximum appears at θ ≈ 0.74π, again matching the predicted critical point. Here the scaling exponent is ≈ 1.4. In both cases, measurements taken far from the critical point yield CFI values that are essentially independent of N, demonstrating the absence of enhancement.

Bayesian analysis of the experimental data yields posterior distributions for θ whose widths approach the quantum Cramér‑Rao bound set by the QFI, indicating near‑optimal estimation performance. The authors report that the estimation error near criticality is roughly half of that obtained away from criticality, confirming the practical advantage of operating at the non‑Hermitian phase transition.

Overall, the paper delivers several key contributions:

• Demonstration of criticality‑enhanced sensing in a non‑unitary system without requiring preparation of the steady state, thereby sidestepping critical slowing down.
• Implementation of both point‑gap and line‑gap topological transitions in a highly controllable photonic quantum‑walk platform, showcasing the versatility of the approach.
• Experimental verification of super‑linear scaling of Fisher information with system size at the transition, a hallmark of quantum‑enhanced metrology.
• Use of Bayesian inference to achieve near‑optimal parameter estimation from experimentally accessible position measurements.

The authors conclude by outlining future directions, including multi‑parameter estimation, extension to higher‑dimensional NH topological models, and integration of the demonstrated principles into practical quantum sensors. Their work bridges the gap between theoretical proposals of criticality‑based quantum metrology and realistic, scalable experimental platforms, opening a pathway toward next‑generation quantum sensing technologies that exploit non‑Hermitian topological phenomena.