Distributed Quantum Sensing

• Distributed Quantum Sensing is the use of entangled quantum resources distributed across spatially separated nodes to estimate a global parameter with enhanced precision.
• It employs architectures such as continuous-variable beam-splitter networks, spin-squeezed atomic ensembles, and time-domain multiplexing to achieve performance improvements over classical limits.
• Recent advancements address practical issues like loss, error correction, and security while integrating sensing with quantum communication networks for scalable, resilient systems.

Searching arXiv for recent and foundational papers on distributed quantum sensing to ground the article in the current literature. Distributed quantum sensing (DQS) is the use of quantum resources across a network of spatially separated sensors to estimate a global property—typically a weighted average or other linear function of locally encoded parameters—with precision beyond the limits of independent sensors. In the formulation emphasized by the DQS review literature, the central contrast is between the standard quantum limit (SQL), where $M$ independent sensors improve sensitivity only as $1/\sqrt{M}$, and entanglement-enabled protocols that can reach $1/M$ Heisenberg scaling for suitable global tasks (Zhang et al., 2020). The field now spans continuous-variable and discrete-variable photonic networks, spin-squeezed atomic ensembles, optical lattices, privacy-preserving and attack-resilient protocols, and newer architectures based on temporal multiplexing, hybrid quantum resources, and causal-order control (Zhuang et al., 2017).

1. Formal setting and performance limits

A standard DQS task estimates a global parameter of the form

$$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$

with $\bm{w}$ a normalized weight vector and $\alpha_m$ locally encoded parameters at $M$ sensing nodes (Zhang et al., 2020). In this setting, the basic metrological benchmark is the distinction between separable-resource networks, whose collective sensitivity improves as $1/\sqrt{M}$, and entangled-resource networks, whose quantum Fisher information (QFI) can scale as $M^2$, giving $1/M$ Heisenberg scaling for appropriate probes and measurements (Zhang et al., 2020).

For continuous-variable displacement sensing with total mean photon number $1/\sqrt{M}$0, a foundational multipartite-entanglement protocol gives the root-mean-square estimation errors

$1/\sqrt{M}$1

for the entangled scheme, and

$1/\sqrt{M}$2

for the product-state scheme (Zhuang et al., 2017). In the lossless limit, the entangled protocol scales as $1/\sqrt{M}$3 whereas the product-state protocol scales as $1/\sqrt{M}$4 (Zhuang et al., 2017).

These bounds encode two durable features of the subject. First, DQS is inherently a global-estimation problem rather than a collection of local estimates. Second, the advantage is task dependent: the metrological gain depends on the target function, resource counting, and the measurement architecture, not merely on the presence of entanglement (Zhang et al., 2020).

2. Canonical architectures and state-engineering strategies

A canonical continuous-variable architecture starts from a single-mode squeezed-vacuum state that is divided equally among $1/\sqrt{M}$5 nodes using a lossless balanced $1/\sqrt{M}$6 beam-splitter array, creating continuous-variable multipartite entanglement. Each node then undergoes parameter encoding and homodyne detection, and a collective estimator combines the local readouts (Zhuang et al., 2017). This construction is important because it uses squeezed-vacuum generation, beam splitters, and homodyne detection, all of which are standard photonic primitives (Zhuang et al., 2017).

The same general beam-splitter-network paradigm underlies experimental four-node continuous-variable phase sensing. In that implementation, a displaced single-mode squeezed state is divided by three balanced beam splitters into four spatial modes, creating a four-mode entangled state; the quantity estimated is the averaged phase shift $1/\sqrt{M}$7, inferred from the average of the measured phase quadratures (Guo et al., 2019). The entangled protocol demonstrates deterministic quantum phase sensing beyond what is attainable with separable probes (Guo et al., 2019).

The resource-engineering landscape has broadened substantially. Hybrid multiphase sensing protocols based on multimode W-type states now combine quantum catalysis, entanglement, and squeezing, with the effective QFI quantified through the QFIM and the associated quantum Cramér–Rao bound

$1/\sqrt{M}$8

where $1/\sqrt{M}$9 is the effective QFI for the global parameter (Zhang et al., 19 May 2026). That work reports that using all three quantum resources gives better sensing performance than using only two under both lossless and lossy conditions, with precision approaching the Heisenberg limit, and that partial quantum catalysis outperforms global catalysis in both ideal and noisy regimes (Zhang et al., 19 May 2026).

Time-domain multiplexing extends the same design philosophy into the temporal domain. A time-multiplexed Gaussian protocol distributes a single squeezed vacuum across $1/M$0 spatial modes and $1/M$1 temporal modes and proves, within the class of Gaussian states, that sensitivity can asymptotically approach

$1/M$2

rather than the earlier $1/M$3 scaling with only linear improvement in $1/M$4 (Yoo et al., 19 Mar 2026). Homodyne detection with maximum-likelihood estimation is shown to asymptotically saturate the quantum Cramér–Rao bound in this setting (Yoo et al., 19 Mar 2026).

3. Loss, readout, repeaters, and error correction

Loss is the central obstacle in DQS. In the continuous-variable multipartite-entanglement protocol, the Heisenberg-scaling advantage is destroyed by loss, although a root-mean-square error advantage remains in moderate-loss regimes (Zhuang et al., 2017). This loss sensitivity is a recurrent theme across optical DQS.

One route around distribution loss is repeater enhancement via noiseless linear amplifiers (NLAs). In repeater-enhanced continuous-variable multipartite sensing, a lossy channel of transmissivity $1/M$5 followed by an NLA of gain $1/M$6 is equivalent to an NLA with effective gain

$1/M$7

before a lossy channel with effective transmissivity

$1/M$8

so that high NLA gain drives $1/M$9 (Xia et al., 2018). The significance claimed there is specific: unlike quantum-repeaters for quantum key distribution, NLA-based repeaters for DQS are argued to be realizable with available technology (Xia et al., 2018).

A second route is continuous-variable quantum error correction. Using GKP-based codes, distributed sensing protocols can restore Heisenberg scaling up to moderate values of $$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$0 in the presence of loss and can also sense both quadratures simultaneously rather than a single quadrature only (Zhuang et al., 2019). For the error-corrected protocol the estimation error is written as

$$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$1

with $$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$2 the logical noise after correction (Zhuang et al., 2019).

A third route is to redesign the readout itself. An all-optical loss-tolerant scheme replaces balanced homodyne detection with phase-sensitive optical parametric amplifiers (OPAs) and linear interferometers (Nehra et al., 2024). In that protocol the quantum signal is directly amplified in the optical domain, the output is measured with a simple power detector, and in the high-gain limit the measurement becomes proportional to the squared amplified quadrature, with a known displacement added to resolve the sign ambiguity (Nehra et al., 2024). The resulting architecture is reported to achieve sensitivity close to the optimal limit set by the QFI of the entangled resource state, to be robust against post-OPA loss, and to exploit optical bandwidths in the tens of terahertz rather than the MHz–GHz limits associated with balanced homodyne electronics (Nehra et al., 2024). This substantially changes the practical bottleneck from electronic bandwidth to optical phase-matching.

4. Experimental realizations across platforms

DQS has progressed from laboratory demonstrations to field tests and non-photonic platforms. The current experimental record is heterogeneous in both resource type and sensing target.

Platform or architecture	Quantum resource	Representative result
Four-node CV optical network	four-mode entangled continuous-variable state	deterministic quantum phase sensing beyond separable probes (Guo et al., 2019)
Field photonic network	polarization-entangled photon pairs	unconditional violation of SNL up to 0.916 dB over 240 m; 10-km fiber demonstration (Zhao et al., 2020)
Spin-squeezed atomic network	nonlocal entanglement from a shared QND measurement	up to 4.5 dB better precision than a network without nonlocal entanglement and 11.6 dB over the quantum projection noise limit (Malia et al., 2022)
Distributed gyroscope network	bright two-mode squeezed states	$$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$3 dB beyond SNL with 5% photon loss and $$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$4 dB initial squeezing (Kannath et al., 2 Aug 2025)

The four-node continuous-variable demonstration showed that the averaged phase shift among four distributed nodes can be estimated with a precision beyond what is attainable with separable probes, using a beam-splitter-generated entangled network and homodyne readout (Guo et al., 2019). The field demonstration then addressed two practical issues at once: real spatial separation and the removal of post-selection. Using entangled photon pairs, it reported unconditional violation of the shot-noise limit by up to 0.916 dB over 240 m, with an average heralding efficiency of 73.88%, and additionally demonstrated operation with 10-km fiber and completely random, unknown parameters (Zhao et al., 2020).

Atomic implementations establish that DQS is not limited to photonic quadrature sensing. In a mode-entangled network of spin-squeezed atomic states, a shared quantum nondemolition measurement entangles up to four spatially distinct atomic modes. The measured performance reaches up to 4.5 dB better precision than a network without nonlocal entanglement and 11.6 dB relative to the quantum projection noise limit, with both atomic clock and atomic interferometer protocols demonstrated (Malia et al., 2022).

Cold-atom optical lattices provide a more structurally distinct example. In a multi-mode tilted Bose–Hubbard system, the metrological limit is given as $$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$5, achieved by the generalized NOON state

$$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$6

and the paper emphasizes that the quadratic dependence on the number of modes does not require correlations between different modes (Pelayo et al., 2022). This is an important counterpoint to the common identification of DQS with multipartite mode entanglement alone.

5. Privacy, security, and integrated network functionality

As DQS moved toward networked deployment, privacy and security became intrinsic rather than auxiliary concerns. One line of work defines privacy with respect to a target function $$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$7: only information about the target function should be accessible, and no other information (Bugalho et al., 2024). Within a QFI-based framework, the privacy measure

$$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$8

satisfies $$\bar{\alpha}=\bm{w}\cdot\bm{\alpha}=\sum_{m=1}^M w_m \alpha_m,$$9 exactly when the QFI matrix is rank-1 and aligned with $\bm{w}$0 (Bugalho et al., 2024). For separable and parallel Hamiltonians, the GHZ state is proved to be the only private pure state for certain linear functions with minimal resources, up to SLOCC, while ancilla-augmented families provide robustness against qubit loss (Bugalho et al., 2024).

A complementary, operational perspective replaces the QFI by the experimentally accessible classical Fisher information matrix (CFIM). In that framework, privacy is linked to the kernel of the CFIM, and the universal privacy quantifier is

$\bm{w}$1

with $\bm{w}$2 the projector onto the support of $\bm{w}$3 (Namkung et al., 27 Jan 2026). In the reported experiment, a protocol using only two photons to estimate four phases yields a singular CFIM whose kernel contains all directions orthogonal to $\bm{w}$4, giving $\bm{w}$5 and Heisenberg-limited precision

$\bm{w}$6

for $\bm{w}$7 photons (Namkung et al., 27 Jan 2026).

Security against adversarial tampering has also been formulated explicitly. A secure and faithful DQS framework under general-coherent attacks introduces single-way and two-way protocols with a safety-threshold mechanism based on the fidelity estimator

$\bm{w}$8

and accepts operation whenever $\bm{w}$9 (Bizzarri et al., 5 May 2025). The single-way protocol is claimed to achieve perfect security, whereas the two-way version guarantees only faithfulness because an adversary may access the encoded parameter on the return channel (Bizzarri et al., 5 May 2025). The LOCC-de-Finetti theorem is used to extend robustness from individual to collective attacks (Bizzarri et al., 5 May 2025).

Network integration adds a different systems-level dimension. The integrated sensing and quantum network (ISAQN) architecture combines CV-QKD with distributed sensing on the same fiber infrastructure, using a round-trip multi-band structure for secure key distribution and the spectrum phase monitoring protocol for sensing (Xu et al., 2024). Its reported performance is approximately 0.7 Mbits/s secret key rate per user over 10 km standard fiber in an 8-user network, together with a vibration response bandwidth from 1 Hz to 2 kHz, 0.50 $\alpha_m$0 strain resolution, and 0.20 m spatial resolution under shot-noise-limited detection (Xu et al., 2024). The sensing component operates at the standard quantum limit rather than beyond it, but the architectural point is the simultaneous realization of communication and sensing in one multi-user quantum network (Xu et al., 2024).

6. Expanding the scope of DQS

The literature no longer restricts DQS to entanglement-assisted phase averaging with a shared phase reference. In the phase-insensitive displacement problem, the relevant regime is a common displacement amplitude with a random global phase that changes from shot to shot. There the achievable precision is determined by first-order normal correlations $\alpha_m$1, and the optimal probes are families of multimode states with definite joint parity that can be read out through local parity measurements (Grochowski et al., 3 Feb 2026). The SQL is $\alpha_m$2, while the quantum advantage obeys

$\alpha_m$3

so the gain grows linearly with the total excitation number even without a global phase reference (Grochowski et al., 3 Feb 2026). This directly broadens DQS from phase sensing to force- and field-amplitude sensing.

Another strand revisits discrete-variable optimal probes. Multi-mode $\alpha_m$4 states have been adapted to DQS for global phase estimation, with both the Cramér–Rao bound and quantum Cramér–Rao bound reaching

$\alpha_m$5

and an experimental four-mode $\alpha_m$6 state achieving a 2.74 dB sensitivity enhancement over the SQL in estimating the average of two spatially distributed phases (Kim et al., 4 Aug 2025). The associated CFIM for the local measurement scheme is diagonal with entries $\alpha_m$7, so the Heisenberg scaling is practically attainable with local operations and photon-number-resolving detection (Kim et al., 4 Aug 2025).

A more radical departure uses causal-order switching rather than entangled probes. In a cyclic free-space optical network, a single probe sequentially queries $\alpha_m$8 independent sensors in opposite causal orders, either as a coherent superposition or as a probabilistic mixture (Xia et al., 21 Jan 2026). The paper attributes the enhancement to the noncommutativity between propagation and sensing processes and derives a quantum Cramér–Rao scaling $\alpha_m$9, experimentally demonstrating distributed beam-tilt sensing with up to 9 sensors and picoradian-scale precision (Xia et al., 21 Jan 2026). Because the main advantage is obtained with a classical mixture of causal orders rather than a quantum switch, the proposal is presented as more feasible than entanglement-intensive alternatives (Xia et al., 21 Jan 2026). A plausible implication is that not all DQS advantages need be organized around multipartite entanglement as the sole nonclassical resource.

Multiparameter saturation has also become explicit. In stroboscopic distributed sensing of mechanically coupled nodes, special times $M$0 eliminate residual probe–oscillator entanglement and permit simultaneous estimation strategies that saturate both the Holevo and quantum Cramér–Rao bounds (Teklu et al., 16 Oct 2025). The reported resource scalings are quadratic, $M$1, for distributed gravimetry and quartic, $M$2, for distributed coupling estimation (Teklu et al., 16 Oct 2025). This addresses a longstanding obstruction in multiparameter metrology, namely the incompatibility of optimal measurements for different parameters.

Taken together, these developments show that DQS has become a broad framework for global estimation in quantum networks rather than a single protocol family. Continuous-variable multipartite entanglement remains the foundational model (Zhuang et al., 2017), but current work also includes hybrid quantum-resource probes (Zhang et al., 19 May 2026), temporal entanglement (Yoo et al., 19 Mar 2026), privacy- and attack-aware architectures (Namkung et al., 27 Jan 2026, Bizzarri et al., 5 May 2025), non-photonic lattice and atomic platforms (Pelayo et al., 2022, Malia et al., 2022), and sensing paradigms that relax the need for shared phase references or entangled probes (Grochowski et al., 3 Feb 2026, Xia et al., 21 Jan 2026). The cumulative pattern suggests that the most durable questions in DQS are no longer only whether entanglement beats the SQL, but which resource, which network architecture, and which operational constraint determine the achievable global precision in realistic distributed systems.