Scaling Enhancement in Distributed Quantum Sensing via Causal Order Switching

TL;DR

This work proposes and experimentally demonstrates a scalable distributed quantum sensing protocol that uses a causal-order switch embedded in a cyclic sensor network. By allowing the probe to interrogate N sensors in a coherent superposition or classical mixture of opposite causal orders, the approach leverages noncommutativity between sensing and propagation to achieve a $1/N^2$ scaling in precision without entangled probes. The combination of a practical classical switch and weak-value amplified readout yields picoradian-scale estimates of the average beam tilt in a free-space network with up to 9 sensors, illustrating a robust route to high-precision quantum sensing networks with reduced entanglement requirements and enhanced practicality.

Abstract

Sensing networks underpin applications from fundamental physics to real-world engineering. Recently, distributed quantum sensing (DQS) has been investigated to boost the sensing performance, yet current schemes typically rely on entangled probes that are fragile to noise and difficult to scale. Here, we propose a DQS protocol that incorporates a causal-order switch into a cyclic network, enabling a single probe to sequentially query N independent sensors in a coherent superposition or a probabilistic mixture of opposite causal orders. By exploiting the noncommutativity between propagation and sensing processes, our scheme achieves a 1/N^2-scaling precision limit without involving entangled probes. Importantly, our approach utilizes a classical mixture of causal orders rather than a quantum switch, making it more feasible for practical realization. We experimentally implement this scheme for distributed beam tilts sensing in a free-space quantum optical network comprising up to 9 sensors, achieving picoradian-scale precision in estimating tilt angle. Our results demonstrate a robust and scalable DQS protocol that surpasses the conventional 1/N Heisenberg scaling in precision, advancing the practical deployment of quantum sensing networks.

Figures (6)

• Figure 1: Schematic of distributed quantum sensing within a cyclic network. a Probe state sequentially queries $N$ sensing nodes in a fixed causal order. b Probe state sequentially queries $N$ sensing nodes in a coherent superposition or a probabilistic mixture of opposite causal orders. An external ancilla, realized either as a qubit (quantum switch) or as a probabilistic mixed state (classical switch), is employed to control the causal order of the probe within the network. The probe state is prepared and the final measurement is performed in the server node.
• Figure 2: Schematic of the experimental scheme with weak value amplification. The ancilla is prepared in the pre-selected state $|i\rangle$, which creates a coherent superposition of opposite causal orders for the probe within the cyclic network. A parity operation is applied to the reverse‑propagation branch, and the ancilla is subsequently projected onto the post-selected state $|f\rangle$, thereby realizing weak value amplification.
• Figure 3: Experimental setup. A $780\nm$ laser beam is coupled into free space using a collimator. The polarization (ancilla) is initialized with a Glan–Taylor polarizer (GTP) and a half-wave plate (HWP). The cyclic sensing network with a coherent superposition of opposite causal orders is realized in a polarizing Sagnac interferometer, where PZT-driven mirrors inside the interferometer serve as the sensors. The number of sensors is set by adjusting the loops and mirrors in the Sagnac interferometer; here we illustrate a configuration with 9 sensors. The final polarization state is post-selected by a polarizer combining with a quarter-wave plate (QWP) to implement the weak value amplification. A Fourier lens and a quadcell photodetector (QPD) are used to measure the transverse momentum of the final probe state.
• Figure 4: Detected spectrums for 1 to 9 sensors. $5\mV$ peak-to-peak driving signals are synchronously applied to the PZT chips of sensors, which corresponds an $11nrad$ beam-tilt modulation in each sensor. The frequency of applied signals is set at $10\kHz$.
• Figure 5: Experimental results of detected signal-to-noise ratio (SNR) at the spectrum analyzer. The applied peak-to-peak voltage is varied from $1\mV$ to $10\mV$ in $1\mV$ increments, corresponding to a loaded average tilt signal from $2.2nrad$ to $22nrad$ in $2.2nrad$ increments. a Experimental results of 1 to 3 sensors configured in the network. b Experimental results of 4 to 6 sensors configured in the network. c Experimental results of 7 to 9 sensors configured in the network. Square markers with error bars stand for the measured SNR; solid lines represent fits to the experimental data.