Distributed Quantum Sensing Achieves 1/N^2 Precision Without Entanglement

Distributed quantum sensing (DQS) holds immense promise for enhancing precision across diverse fields, but current methods often struggle with scalability and noise susceptibility. Researchers Binke Xia (The University of Hong Kong), Zhaotong Cui and Jingzheng Huang (Shanghai Jiao Tong University), alongside Yuxiang Yang and Guihua Zeng et al, have now demonstrated a significant leap forward by developing a DQS protocol that bypasses the need for fragile entangled probes. Their innovative approach utilises a causal-order switch within a cyclic network, allowing a single probe to efficiently query multiple independent sensors, achieving a remarkable 1/N² scaling in precision. This breakthrough, experimentally validated in a free-space optical network with up to nine sensors and achieving picoradian-scale tilt angle estimation, not only surpasses the conventional Heisenberg limit but also offers a more robust and practically realisable pathway towards advanced sensing networks.

Theoretical analysis confirms that this probabilistic mixture of pure strategies yields superior performance compared to individual pure strategies, a rare outcome in quantum metrology. The research establishes a new benchmark in precision sensing, demonstrating a significant enhancement over the conventional quantum limit.

By leveraging weak value amplification alongside the causal-order switching, the team further boosted practical precision, paving the way for real-world applications. This breakthrough opens exciting possibilities for deploying quantum sensing networks in diverse fields, including interferometric alignment, vibration monitoring, and acoustic sensing, areas demanding extremely high sensitivity and precision. The team achieved this enhanced precision by mapping the average momentum kick experienced by the probe directly onto an additional spatial shift, amplified by a factor containing an N² term. This amplification effect is a direct consequence of the non-commutative nature of the sensing and propagation processes, and the clever implementation of the causal-order switch. Consequently, the work not only demonstrates a fundamental advance in quantum sensing but also provides a pathway towards building practical, scalable, and robust sensing networks for a wide range of scientific and engineering applications. The demonstrated prad-scale beam-tilt sensitivity represents a significant step forward in the field of quantum metrology and promises to unlock new capabilities in precision measurement.

Causal Switching for Distributed Quantum Sensing enables enhanced

To establish the experimental setup, the researchers constructed an interferometer utilising an odd number of mirrors, both piezo-driven and static, to ensure a parity transformation regarding the probe state’s reverse propagation direction; this configuration was essential for weak value amplification (WVA). An initial ancilla state |i⟩ was prepared using a linear polarizer and a half-wave plate (HWP), while the post-selection state |f⟩ was realised with a quarter-wave plate (QWP) and another linear polarizer, with the post-selection angle ε adjusted to achieve a fixed weak value of |Aw| ≈7. A “sandwich” configuration, comprising two QWPs and one HWP, compensated for the additional relative phase introduced by the interferometer, details of which are available in the Supplemental Materials. The core measurement relied on quantifying differential intensity, I∆, defined as the difference between the detected intensity on the left (IL) and right (IR) halves of a quadrant photodiode (QPD), which determined the central position of the final received beam.

The measured value, Mf, corresponded directly to I∆, and the QPD established a relationship of Mf = 0.65(I∆/I0) × beam radius, where I0 represents the total intensity received. This allowed the team to determine the sensing parameter θ via the equation I∆= 2I0 1.3εw0 h z 2k N 2 + z 2k + zin k N i θ, linking the measured intensity difference to the tilt angle. Experiments involved applying synchronized 10kHz sinusoidal drive signals to piezoelectric transducers (PZTs) at each sensing node, inducing a beam-tilt modulation of 11 nrad per 5mV peak-to-peak drive. The QPD converted the differential optical power, I∆, into an electrical signal, which was then analysed using a spectrum analyser to extract the 10kHz component corresponding to the average tilt φ. The team stabilized the received optical power I0 at approximately 0.2mW and observed that the peak levels at 10kHz increased nonlinearly with the number of sensors, enabling the estimation of the noise floor and signal-to-noise ratio (SNR). The minimum detectable angular tilt δ φmin satisfied the relation δ φmin ∝ 1 N 2 + (1 + 2zin/ z)N, demonstrating an improvement in precision scaling nonlinearly with the number of sensors.

Non-entangled probes achieve 1/N² sensing precision, while entangled

The team’s work surpasses conventional 1/N Heisenberg scaling, paving the way for more robust and scalable sensing networks. Data shows the successful application of this technique to distributed beam tilts sensing, a crucial capability for various engineering and physics applications. The breakthrough delivers a nonlinear scaling enhancement, meaning that as the number of sensors increases, the precision improves at an accelerated rate, specifically, precision scales inversely with the square of the number of sensors (1/N^2). Scientists recorded a substantial enhancement in sensing performance by leveraging the interplay between probe propagation and the sensing process itself.

Tests prove that the sequential querying strategy, combined with the network architecture, effectively amplifies the sensing signal, leading to the observed 1/N^2 scaling. The team utilized photon polarization as a switch ancilla, enabling control over the probe’s propagation direction and facilitating the implementation of the causal-order switching strategy. Measurements confirm that the average momentum kick experienced by the probe is directly mapped onto a spatial shift, amplified by a factor containing the N^2 term, which is critical for achieving the enhanced precision. The experimental setup employed weak value amplification (WVA) to further improve the practical precision of the measurements.

Causal Switching Boosts Quantum Sensing Precision by minimizing

Current DQS methods often depend on entangled probes, which are susceptible to noise and challenging to scale for complex networks. The authors acknowledge a limitation in that the current experimental setup is confined to free-space optical networks, and extending the protocol to other modalities may require further development. Future research directions, as suggested by the team, include exploring the application of this DQS protocol to more complex sensing scenarios and investigating its potential for integration with other quantum technologies. These advancements could significantly impact fields reliant on high-precision measurements, such as fundamental physics, metrology, and engineering applications.