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arxiv: 2606.02416 · v1 · pith:YEUWEYHEnew · submitted 2026-06-01 · 🪐 quant-ph

Bounds on Nonlocality and Random Access Codes from Extended Information Causality Principle

Prabhav Jain , Nikolai Miklin , Mariami Gachechiladze This is my paper

Pith reviewed 2026-06-28 13:48 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Information CausalityBell inequalitiesrandom access codesnonlocal correlationsquantum boundsCollins-Gisin inequalities
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The pith

Extended Information Causality produces stronger Bell inequalities and new bounds on random access codes

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

The paper establishes that an extension of the Information Causality principle, which permits correlations among one party's measurement choices, produces a family of new quantum Bell inequalities. These inequalities provide stronger constraints than those from the original principle and lead to an improved analytical bound for the Collins-Gisin inequalities. When the same extended principle is applied to entanglement-assisted random access codes, it yields analytical bounds on the winning probability that match those from the original principle, indicating that the original bounds are optimal for this setting.

Core claim

By extending Information Causality to include correlations among Alice's inputs, the authors derive a family of Bell inequalities that strengthen previous constraints on quantum correlations. These are used to obtain an improved analytical bound for the Collins-Gisin family. Application to entanglement-assisted random access codes produces new theory-independent bounds on the winning probability, but the extension does not tighten them beyond the original Information Causality bounds.

What carries the argument

The extended Information Causality principle allowing correlations among Alice's inputs

If this is right

  • Stronger constraints apply to nonlocal correlations in Bell scenarios with more than binary inputs and outputs.
  • An improved analytical upper bound holds for the quantum value of the Collins-Gisin family of Bell inequalities.
  • New theory-independent analytical bounds exist on the winning probability of entanglement-assisted random access codes.
  • The original Information Causality principle already achieves optimal bounds for the class of binary random access codes considered.

Where Pith is reading between the lines

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

  • The optimality for random access codes suggests that further refinements of the principle may be needed to constrain quantum correlations more tightly in communication tasks.
  • Applying the extended principle to other nonlocality scenarios could uncover additional bounds not captured by the original formulation.
  • Experimental tests of the new Bell inequalities could distinguish whether the extension correctly describes physical correlations.

Load-bearing premise

The extended Information Causality principle correctly describes a valid constraint on physical nonlocal correlations.

What would settle it

A quantum correlation that violates one of the new Bell inequalities derived from the extended principle while satisfying all known quantum bounds would falsify the claim that the principle constrains quantum theory.

Figures

Figures reproduced from arXiv: 2606.02416 by Mariami Gachechiladze, Nikolai Miklin, Prabhav Jain.

Figure 1
Figure 1. Figure 1: FIG. 1. The communication scenario. Alice receives a string [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. A comparison of the inequalities obtained from the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Plot of critical values of [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
read the original abstract

Information Causality was introduced as a physical principle for constraining the set of nonlocal correlations. In recent work, we proposed an extension of Information Causality that allows correlations among Alice's inputs. This extended principle yields tighter constraints than the original formulation and recovers part of the quantum boundary in certain Bell scenarios. In this work, we further investigate the implications of extended Information Causality and apply it to scenarios beyond binary inputs and outputs. We derive a family of quantum Bell inequalities that strengthen previously known constraints on quantum correlations. Using these inequalities, we obtain an improved analytical bound for the Collins-Gisin family of Bell inequalities. We also apply Information Causality to entanglement-assisted random access codes and derive new theory-independent analytical bounds on the winning probability. For this latter task, we prove that, despite being stronger in general, the extended principle does not improve the bounds obtained from the original Information Causality principle. This suggests that the existing Information Causality bounds are optimal for this class of random access codes.

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

0 major / 1 minor

Summary. The manuscript extends the Information Causality principle to allow correlations among Alice's inputs. It derives a family of quantum Bell inequalities that strengthen previously known constraints, obtains an improved analytical bound for the Collins-Gisin family, and applies the principle to entanglement-assisted random access codes to derive new theory-independent bounds on winning probability. It proves that the extended principle yields no improvement over the original for this class of random access codes.

Significance. If the derivations and proof hold, the work strengthens theory-independent bounds on nonlocal correlations in Bell scenarios and establishes optimality of existing Information Causality bounds for entanglement-assisted random access codes. The explicit derivations of the extended bounds and the proof that the extension does not tighten the RAC results are strengths that advance the program of using physical principles to constrain quantum correlations.

minor comments (1)
  1. The comparison between the original and extended Information Causality principles in the introduction would benefit from an explicit side-by-side equation or table to highlight the modification allowing input correlations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment and recommendation to accept the manuscript. The referee's summary correctly identifies the main results on the extended Information Causality principle, the strengthened Bell inequalities, the improved bound for the Collins-Gisin family, and the proof that the extension yields no further tightening for entanglement-assisted random access codes.

Circularity Check

0 steps flagged

Minor self-citation to prior definition of extended principle; all new derivations are explicit and non-reductive

full rationale

The manuscript cites the authors' own recent work solely to introduce the definition of the extended Information Causality principle (allowing input correlations). All subsequent steps—deriving a family of strengthened Bell inequalities, obtaining an improved analytical bound on the Collins-Gisin family, and proving that the extension yields no tighter RAC bounds—are presented as direct, explicit computations from the stated principle. No equation reduces a claimed prediction to a fitted parameter, no uniqueness theorem is imported from self-citation, and no ansatz is smuggled via citation. The self-citation is therefore not load-bearing for the new results and does not create circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the extended Information Causality principle as a physical constraint. No free parameters or new physical entities are introduced in the abstract.

axioms (1)
  • domain assumption Information Causality (original and extended) is a valid physical principle that constrains nonlocal correlations
    The entire analysis builds directly on this principle and its extension.

pith-pipeline@v0.9.1-grok · 5705 in / 1195 out tokens · 32846 ms · 2026-06-28T13:48:40.107133+00:00 · methodology

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Reference graph

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