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arxiv: 2604.11910 · v1 · submitted 2026-04-13 · 🪐 quant-ph

Network Nonlocality with Separable Measurements

Emanuele Polino , Davide Poderini , Giorgio Minati , Giovanni Rodari , Rafael Chaves , Fabio Sciarrino This is my paper

Pith reviewed 2026-05-10 15:47 UTC · model grok-4.3

classification 🪐 quant-ph
keywords network nonlocalityseparable measurementsquantum networksclassical feedforwarddevice-independent randomnessminimal network nonclassicalityindependent sources
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The pith

Separable measurements plus bidirectional classical feedforward can produce correlations that certify full network nonlocality without any entangled detectors.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that full network nonlocality, which certifies nonclassical behavior from every independent source in a quantum network, does not require entangled measurements at any node. The authors give an explicit construction in which separable measurements, combined with classical signals sent both ways between the central node and the outer nodes, generate the necessary correlations. This matters because entangled measurements have been a major experimental obstacle in previous network nonlocality tests. The same measurement class is also shown to certify the weaker notion of minimal network nonclassicality and to support device-independent randomness extraction. By removing the need for entangled detectors, the strategy points toward simpler laboratory realizations of network nonlocality.

Core claim

The central claim is that an explicit strategy based on separable measurements augmented with bidirectional classical feedforward achieves full network nonlocality for networks with independent sources, certifying the nonclassicality of every source without relying on entangled measurements at the central node.

What carries the argument

Separable measurements augmented with bidirectional classical feedforward, which let the central node exchange classical information with peripheral nodes to produce correlations that certify every source as nonclassical.

If this is right

  • Full network nonlocality can be demonstrated without performing entangled measurements.
  • The same class of measurements also certifies minimal network nonclassicality.
  • Device-independent randomness can be extracted and quantified from full network nonlocal correlations under separable measurement strategies.
  • Experimental tests of network nonlocality become feasible with simpler, non-entangled detectors.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach may generalize to other network shapes where entangled measurements were previously required.
  • Classical communication can substitute for some quantum resources in certifying network nonlocality, which could simplify resource accounting in quantum networks.
  • Larger or more complex networks might now be testable in the lab because detector entanglement is no longer needed.

Load-bearing premise

The correlations generated by this separable-plus-feedforward strategy cannot be reproduced by any classical model with independent sources.

What would settle it

Deriving a classical local hidden-variable model that exactly matches the output statistics of the proposed separable measurements with bidirectional feedforward would show that full network nonlocality has not been achieved.

Figures

Figures reproduced from arXiv: 2604.11910 by Davide Poderini, Emanuele Polino, Fabio Sciarrino, Giorgio Minati, Giovanni Rodari, Rafael Chaves.

Figure 1
Figure 1. Figure 1: Bilocality scenarios. a) with an external input per measurement station; b) with external inputs only in the exter￾nal nodes; c) when the second source λ2 shares a no-signaling (NS) resource (red dotted square); d) when the first source λ1 shares an NS resource. challenging to realize efficiently in quantum optics [71, 72], and avoiding them can improve robustness and practical feasibility, for instance by… view at source ↗
Figure 2
Figure 2. Figure 2: Measurement entanglement-free strategy. a) Scheme of the entanglement-free, feedback-based strategy to demonstrate FNN in the bilocal scenario. The measurement in the central node consists of two alternating feedback-based measurements, each occurring half of the time. The half circle in yellow shows the feedback from the subsystem of the source connecting A and B, determining the measurement on the subsys… view at source ↗
Figure 3
Figure 3. Figure 3: Nonclassicality with feedback-based measurements. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Randomness certification comparison between the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

Quantum correlations in networks with independent sources have revealed novel forms of nonclassical behavior. While entanglement in the sources is a necessary ingredient, the role played by entanglement in the measurements remains largely unexplored. In particular, all existing demonstrations of full network nonlocality, certifying the nonclassicality of every source in the network, have relied on entangled measurements performed at a central node with no inputs. In this work, we construct an explicit strategy that does not rely on entangled measurements, yet still achieves full network nonlocality. Our approach is based on separable measurements augmented with bidirectional classical feedforward. We further show that this same class of measurements can give rise to another recently proposed form of network nonlocality, the minimal network nonclassicality, which ensures that the observed correlations cannot be attributed to any fixed subset of nonclassical sources within the network. Finally, building on a recently developed certification framework, we quantify the amount of device-independent randomness that can be extracted from full network nonlocal correlations under different measurement strategies. Beyond their foundational significance, our results also offer a practically attractive route toward experimental implementations of network nonlocality, as they remove the need for entangled measurements.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript constructs an explicit strategy using separable measurements augmented with bidirectional classical feedforward that achieves full network nonlocality (certifying nonclassicality of every independent source) without entangled measurements at the central node. It further shows that the same class of measurements can produce minimal network nonclassicality and applies an existing certification framework to quantify the device-independent randomness extractable from the resulting correlations.

Significance. If the explicit construction holds, the result is significant for both foundational and practical reasons: it removes the requirement for entangled measurements in demonstrations of full network nonlocality, thereby offering a more experimentally accessible route, while the extension to minimal network nonclassicality and the randomness quantification strengthen device-independent protocols in networks with independent sources. The explicit, parameter-free nature of the strategy (as asserted) is a notable strength.

major comments (2)
  1. [§3] §3 (the explicit construction): the central claim that separable measurements plus bidirectional feedforward suffice to violate all classical bounds for full network nonlocality is load-bearing; the manuscript must supply the concrete POVM elements, the precise feedforward rules, and the resulting correlation expressions so that the violation can be verified directly against the classical polytope for the assumed network topology.
  2. [§5] §5 (randomness quantification): the application of the existing certification framework to the separable-measurement case must explicitly state how the feedforward affects the min-entropy bound and whether the bound remains tight relative to the entangled-measurement case; without this, the comparative claim cannot be assessed.
minor comments (2)
  1. [Abstract/Introduction] The abstract and introduction should briefly specify the network topology (number of sources, parties, and inputs) used for the construction to improve readability.
  2. [§3] Notation for the bidirectional classical feedforward should be defined once at first use and used consistently; a small diagram would clarify the information flow.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the work, and recommendation for minor revision. We address each major comment below, indicating the revisions that will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (the explicit construction): the central claim that separable measurements plus bidirectional feedforward suffice to violate all classical bounds for full network nonlocality is load-bearing; the manuscript must supply the concrete POVM elements, the precise feedforward rules, and the resulting correlation expressions so that the violation can be verified directly against the classical polytope for the assumed network topology.

    Authors: We agree that explicit, verifiable details are essential for the central claim in §3. While the manuscript already outlines the separable measurement strategy and bidirectional feedforward protocol in sufficient detail to define the correlations, we will add a new appendix in the revised version. This appendix will provide the concrete POVM elements (as product operators on the local Hilbert spaces), the precise rules for what classical information is communicated in each direction based on local outcomes, and the full analytic expressions for the resulting tripartite correlations p(a,b,c|x,y,z). These expressions will be directly compared to the relevant facets of the classical polytope for the network with independent sources, allowing immediate numerical verification of the violation. We believe this addition will fully address the concern without altering the main text. revision: yes

  2. Referee: [§5] §5 (randomness quantification): the application of the existing certification framework to the separable-measurement case must explicitly state how the feedforward affects the min-entropy bound and whether the bound remains tight relative to the entangled-measurement case; without this, the comparative claim cannot be assessed.

    Authors: We agree that the impact of feedforward on the min-entropy bound requires explicit clarification. In the revised §5 we will add a dedicated paragraph explaining that bidirectional classical feedforward is incorporated into the certification framework by treating the communicated messages as additional classical inputs that define the effective local response functions at each node. The min-entropy is then lower-bounded directly from the observed correlations (which already include all feedforward effects) using the same semidefinite programming relaxation as in the entangled-measurement case. Because the framework depends only on the network structure and the observed joint distribution, the resulting bound is identical for any implementation that produces the same correlations; we will include a side-by-side numerical comparison confirming that the extractable randomness is the same (and remains tight) relative to the entangled-measurement strategy. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents an explicit construction of a separable measurement strategy augmented with bidirectional classical feedforward to achieve full network nonlocality, without relying on entangled measurements. This is a direct existence proof via construction rather than any reduction to fitted inputs, self-definitional loops, or load-bearing self-citations. The abstract and provided description show the central claim stands independently as a strategy that certifies nonclassicality for all sources, with no evidence of the enumerated circular patterns such as renaming known results or smuggling ansatzes via prior self-work. The derivation is self-contained against the network topology and measurement assumptions stated.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard quantum mechanics for networks with independent sources and the existence of a specific separable measurement strategy with classical feedforward.

axioms (1)
  • domain assumption Standard quantum mechanics governs the network with independent sources and local operations
    The work assumes quantum theory applies to describe the correlations and that sources are independent.

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discussion (0)

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