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arxiv: 2605.21293 · v1 · pith:VZG5RBALnew · submitted 2026-05-20 · 🪐 quant-ph

Quantum Nonlocality and Device-Independent Randomness are Robust to Noisy Signaling Channels

Kuntal Sengupta , Lewis Wooltorton This is my paper

Pith reviewed 2026-05-21 04:27 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Bell inequalitiesquantum nonlocalitydevice-independent randomnessnoisy signalinglocal polytopeCHSH inequalityrandomness certification
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The pith

Bell inequalities can still certify quantum nonlocality and device-independent randomness even when one party receives a noisy copy of the other's input through a signaling channel.

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

The paper investigates whether quantum nonlocality remains detectable when the strict no-signaling condition of Bell tests is relaxed to allow noisy transmission of inputs between the two parties. It models the imperfection as a binary channel that forwards a noisy version of one input before measurements occur. By fully mapping the local polytope in this relaxed setting, the authors derive new Bell inequalities that quantum correlations can violate even when the channel noise is low. These inequalities outperform the standard CHSH inequality in extracting certified randomness under additional depolarizing noise on the quantum state. The same approach extends to the case where both parties exchange noisy input copies.

Core claim

If a binary channel sends a noisy copy of one party's input to the other before any measurements take place, Bell inequalities exist that certify non-signaling quantum correlations. This holds even when a near perfect copy of the input is sent. The local polytope in this scenario is completely characterized by its vertices and facets, allowing identification of such inequalities. These inequalities are more robust to depolarizing noise than the CHSH inequality when certifying device-independent randomness. Similar conclusions hold when both parties receive noisy copies of each other's inputs.

What carries the argument

The local polytope under noisy input signaling via a binary channel, fully characterized by its vertices and facets to derive Bell inequalities that bound classical behaviors while remaining violated by quantum correlations.

If this is right

  • Quantum nonlocality can be certified from observed data even when devices allow limited input leakage through noisy channels.
  • Device-independent randomness extraction remains feasible and yields higher rates with the new inequalities than with CHSH under depolarizing noise.
  • The full characterization of the local polytope enables systematic search for optimal inequalities in this signaling model.
  • Similar robustness conclusions apply when both parties receive noisy copies of each other's inputs.

Where Pith is reading between the lines

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

  • These inequalities could support device-independent protocols in compact physical setups where perfect isolation of inputs is impractical.
  • Optimizing the inequalities for particular channel noise strengths may further improve certified randomness yields in noisy environments.
  • The polytope enumeration technique opens a route to analyze noisy signaling in multipartite or higher-dimensional Bell scenarios.

Load-bearing premise

The imperfect signaling can be accurately modeled as a binary channel transmitting a noisy copy of one input to the other party prior to any measurements.

What would settle it

Compute the maximum value of one of the new Bell inequalities achievable by quantum mechanics under a chosen noisy channel parameter and verify whether it exceeds the local bound obtained from the polytope facets; violation by quantum but not by the enumerated local vertices would support the claim.

Figures

Figures reproduced from arXiv: 2605.21293 by Kuntal Sengupta, Lewis Wooltorton.

Figure 1
Figure 1. Figure 1: FIG. 1. An illustration of the minimal Bell scenario in the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison between different Bell expression when [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Value of the parameter [PITH_FULL_IMAGE:figures/full_fig_p034_4.png] view at source ↗
read the original abstract

Given a pair of isolated devices that accept random binary inputs and return binary outputs, a user can deduce from the observed data alone if the underlying mechanism can be explained classically. Bell's theorem further states that a classical explanation can be ruled out if the devices perform certain measurements on an entangled quantum state, underpinning the security of cryptographic protocols that are device-independent (DI). For certain protocols, such as those performed in a tight space, it might be difficult to perfectly enforce the non-signaling assumption required in Bell's theorem. This prompts the question: is quantum nonlocality robust to such imperfections? We show that if a binary channel sends a noisy copy of one party's input to the other before any measurements take place, the answer is yes. We completely characterize the vertices and facets of the local polytope in this scenario, and identify Bell inequalities that certify non-signaling quantum correlations. This is possible even when a near perfect copy of the input is sent. We go on to show that the identified inequalities are more robust to depolarizing noise than the Clauser-Horne-Shimony-Holt inequality when certifying DI randomness in this scenario. In addition, we characterize the local polytope when both parties receive a noisy copy of each other's input and make similar conclusions, leaving many new potential Bell inequalities to be explored.

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 / 3 minor

Summary. The manuscript studies the robustness of quantum nonlocality and device-independent randomness extraction to imperfect isolation in Bell scenarios. It models a one-way noisy binary channel that transmits a copy of Alice's input to Bob prior to measurement, fully characterizes the vertices and facets of the resulting local polytope, and identifies Bell inequalities that remain violated by non-signaling quantum correlations even for near-perfect channel fidelity. The authors further compare the noise robustness of these inequalities against CHSH for DI randomness certification and extend the polytope analysis to the bidirectional noisy-signaling case.

Significance. If the claimed complete polytope characterization is accurate, the result is significant for practical device-independent protocols, as it demonstrates that nonlocality and randomness certification can persist under realistic signaling imperfections that are difficult to eliminate in compact setups. The explicit facet inequalities and their superior performance under depolarizing noise relative to CHSH provide concrete, usable tools for improving security margins in DI randomness generation. The bidirectional extension opens additional avenues for inequality discovery.

major comments (2)
  1. [§4] §4 (Characterization of the one-way local polytope): The central claim of a complete vertex enumeration for the local polytope under the probabilistic noisy channel rests on exhaustive listing of channel-compatible deterministic strategies, yet the manuscript provides no explicit count of total strategies considered, no verification algorithm, and no supplementary data confirming that the reported vertices form the full convex hull. This enumeration is load-bearing for the subsequent facet extraction and for the assertion that the identified inequalities certify non-signaling quantum correlations.
  2. [Table 2] Table 2 (Facet inequalities for near-perfect channel): The listed inequalities are stated to remain violated by quantum correlations at high channel fidelity, but no explicit calculation or reference to the quantum violation value is supplied for the specific channel parameter regime claimed to be 'near perfect,' undermining the robustness statement without additional verification steps.
minor comments (3)
  1. [Eq. (7)] The notation for the noisy channel transition probabilities in Eq. (7) is introduced without a clear diagram or example computation showing how a deterministic local strategy maps to the four possible output tables.
  2. [Figure 3] Figure 3 caption does not specify the exact depolarizing noise parameter range used for the robustness comparison, making it hard to reproduce the plotted advantage over CHSH.
  3. [Introduction] A reference to the standard Bell polytope methods (e.g., from prior works on signaling polytopes) is missing in the introduction, which would help situate the new enumeration technique.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and will revise the manuscript to provide the requested details on the polytope enumeration and explicit quantum violation values.

read point-by-point responses

  1. Referee: [§4] §4 (Characterization of the one-way local polytope): The central claim of a complete vertex enumeration for the local polytope under the probabilistic noisy channel rests on exhaustive listing of channel-compatible deterministic strategies, yet the manuscript provides no explicit count of total strategies considered, no verification algorithm, and no supplementary data confirming that the reported vertices form the full convex hull. This enumeration is load-bearing for the subsequent facet extraction and for the assertion that the identified inequalities certify non-signaling quantum correlations.

    Authors: We agree that additional transparency on the enumeration strengthens the claim. The local polytope vertices were obtained by exhaustive enumeration of all 16 deterministic local strategies (4 response functions for Alice and 4 for Bob, given binary inputs/outputs). For each strategy we computed the induced behavior under the probabilistic one-way channel and extracted the extreme points of their convex hull. In the revised manuscript we will state the total count explicitly, describe the enumeration procedure, and include the full list of vertices (or a supplementary table) to allow independent verification that they span the reported convex hull. revision: yes

  2. Referee: [Table 2] Table 2 (Facet inequalities for near-perfect channel): The listed inequalities are stated to remain violated by quantum correlations at high channel fidelity, but no explicit calculation or reference to the quantum violation value is supplied for the specific channel parameter regime claimed to be 'near perfect,' undermining the robustness statement without additional verification steps.

    Authors: We acknowledge that explicit numerical values would make the robustness claim easier to verify. In the revised version we will add the quantum violation amounts (obtained via semidefinite programming or Tsirelson-bound optimization) for each inequality in Table 2 at the high-fidelity regimes discussed (e.g., channel fidelity 0.99). These calculations confirm that the new inequalities remain violated while CHSH does not, and we will include the relevant SDP formulations or references. revision: yes

Circularity Check

0 steps flagged

No significant circularity in polytope characterization or inequality identification

full rationale

The paper's derivation proceeds by defining a noisy binary signaling channel model, enumerating deterministic local strategies compatible with that channel to obtain the vertices of the resulting local polytope, extracting its facets as Bell inequalities, and then verifying that certain quantum correlations violate those inequalities. This is a standard, non-reductive application of convex geometry to an explicitly stated scenario; the enumeration and facet extraction supply independent content rather than renaming or fitting inputs. No self-definitional loops, fitted parameters presented as predictions, or load-bearing self-citations appear in the provided text. The claimed robustness result therefore rests on the explicit model and computation rather than tautological equivalence to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on standard convex polytope theory and the modeling choice of a binary noisy channel; no free parameters, new entities, or ad-hoc axioms are introduced in the abstract.

axioms (1)
  • standard math Local behaviors form a convex polytope whose vertices and facets can be enumerated under modified signaling constraints.
    Invoked when the authors state they completely characterize the vertices and facets of the local polytope.

pith-pipeline@v0.9.0 · 5766 in / 1109 out tokens · 28357 ms · 2026-05-21T04:27:05.675156+00:00 · methodology

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    F acets ofS (p,p),(1/2,1/2) F1 =   1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   ,F 2 =   1− 1−p 2p−1 0 0 1− 1−p 2p−1 0 0 0− p−1 2p−1 0 0 0− p−1 2p−1 0 0   , F3 =   1− −3p3+4p2−3p+1 4p3−4p2+3p−1 0− p3 4p3−4p2+3p−1 − −5p3+5p2−3p+1 4p3−4p2+3p−1 − −4p3+3p2−2p+1 4p3−4p2+3p−1 (p−1)2p 4p3−4p2+3p−1 0 0− (p−1)3 4p3−4p2+3p−1 0− p3−p2 4p3−4p2+3p−1 0− p3−p...

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    F acets ofS (p,p),(p,p) F′ 1 =   1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   , F′ 2 =   p 2p−1 p 2p−1 p−1 2p−1 p−1 2p−1 0 0 0 0 0 0 0 0 0 0 0 0   , F′ 3 =   1− −3p3+2p2−2p+1 4p3−4p2+3p−1 0 (p−1)p2 4p3−4p2+3p−1 − −3p3+2p2−2p+1 4p3−4p2+3p−1 − −2p3+2p2−2p+1 4p3−4p2+3p−1 − (p−1)3 4p3−4p2+3p−1 0 0− (p−1)3 4p3−4p2+3p−1 0− −p3+2p2−p 4p3−4p2+3p−1 0− (p−...

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    On the other hand,vrefers to a facet for which there is numerical evidence that a non-signaling two-qubit strategy violates the corresponding facet inequality

    F acets ofS (p,1),(r,1) In the subscript,srefers to a facet for which numerical evidence suggests no quantum violation is possible using two-qubit strategies. On the other hand,vrefers to a facet for which there is numerical evidence that a non-signaling two-qubit strategy violates the corresponding facet inequality.   1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

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    Therefore, for simplicity here we taker=p

    Examples of interesting facets ofS (p,1)∗,(r=p,1)∗ Note that for anyp, r∈[0,1),S (p,1)∗,(r,1)∗ ⊆S (p=p′,1)∗,(r=p′,1)∗, wherep ′ := max{p, r}. Therefore, for simplicity here we taker=p. We numerically found 5 interesting facets of this polytope, i.e., ones that indicate a quantum violation following a numerical search. We managed to derive the following tw...

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    For all non-signaling local behaviorsP NS L ,T p(PNS L )⩽2(|2p−1|+ 1−p)/p

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    For all one-way signaling local behaviorsP S L ∈S (p,p),(1/2,1/2),T p(PS L)⩽2 max n p, −p+ 2 (1−p)2 p o + 2(1−p)

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    For all non-signaling quantum behaviorsP NS Q ,T p(PNS Q )⩽2 √ 2 q p 3p−1

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    (F3) whenp∈(2/5,1/2)∪(1/2,1)andθ=ϕ=−π/4whenp= 1/2

    Up to local isometries, there is a unique non-signaling quantum strategy that achievesT p(PNS Q ) = 2 √ 2 q p 3p−1, given by ρ=|ψ θ⟩ ⟨ψθ|,|ψ θ⟩= cos(θ)|00⟩+ sin(θ)|11⟩, A0 =σ X , A 1 =σ Z, B0 = cos(ϕ)σ Z + sin(ϕ)σ X , B1 =−cos(ϕ)σ Z + sin(ϕ)σ X , (F2) where θ= 1 2arctan f1/g1 −π/2, ϕ= arctan f2/g2 , f1 = p p(−2 + 5p) 1−3p , g 1 = 1−2p −1 + 3p, f2 =− r −2 ...

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    For all two-way signaling local behaviorsP S L ∈S (p,1),(r,1),W p,r(PS L)⩽1

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    There exists a non-signaling quantum behaviorP NS Q such thatW p,r(PS Q)>1. Proof.Part 1: As done in the proof of Proposition 1, we can parameterise a LHV model using 8±1 valued variables αx,y = (−1)ax,y andβ x,y = (−1)bx,y forx, y∈ {0,1}, wherea x,y andb x,y are the binary response functions. We then define ⟨Ax,0⟩=rα x,0 + (1−r)α x,1 ⟨Ax,1⟩=α x,1 ⟨B0,y⟩=...

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