Noise-Resilient Heisenberg-limited Quantum Sensing via Indefinite-Causal-Order Error Correction

TL;DR

This paper introduces a novel quantum error correction protocol using indefinite causal order to achieve Heisenberg-limited sensing in noisy environments, surpassing traditional limitations.

Contribution

It presents the first application of indefinite causal order in quantum error correction, enabling real-time error correction without prior noise knowledge or measurement-based syndrome extraction.

Findings

Restores Heisenberg-limited scaling in noisy quantum sensors

Demonstrates error correction in single-qubit, many-body, and continuous-variable systems

Identifies regimes with measurement-free, unitary error correction

Abstract

Quantum resources can, in principle, enable Heisenberg-limited (HL) sensing, yet no-go theorems imply that HL scaling is generically unattainable in realistic noisy devices. While quantum error correction (QEC) can suppress noise, its use in quantum sensing is constrained by stringent requirements, including prior noise characterization, restrictive signal-noise compatibility conditions, and measurement-based syndrome extraction with global control. Here we introduce an ICO-based QEC protocol, providing the first application of indefinite causal order (ICO) to QEC. By coherently placing auxiliary controls and noisy evolution in an indefinite causal order, the resulting noncommutative interference enables an auxiliary system to herald and correct errors in real time, thereby circumventing the limitations of conventional QEC and restoring HL scaling. We rigorously establish the protocol for single- and multi-noise scenarios and demonstrate its performance in single-qubit, many-body, and continuous-variable platforms. We further identify regimes in which error correction can be implemented entirely by unitary control, without measurements. Our results reveal ICO as a powerful resource for metrological QEC and provide a broadly applicable framework for noise-resilient quantum information processing.