This version substantially revises and extends the March 2026 preprints on persistence under Information Causality. The manuscript reformulates the analysis around the exact information score of the canonical concatenated binary random-access-code protocol and develops an exact positive-series representation that leads to rigorous finite-depth bounds. These results establish a complete subcritical, critical, and supercritical classification of the concatenated Information-Causality dynamics. Correlations below the Tsirelson point exhibit asymptotic loss of accumulated information; correlations above it eventually violate Information Causality at finite depth; and the Tsirelson point is uniquely characterized by finite, nonzero asymptotic informational persistence. The new version also provides controlled finite-depth corrections at criticality, a rigorous treatment of the critical remainder, a mathematical branching generalization, a local Fisher-information interpretation of the quadratic scaling, and a universality result for smooth symmetric information-divergence measures. Numerical stability near the critical regime is treated explicitly. Compared with the March versions, the present manuscript therefore replaces the primarily asymptotic stability argument with a stronger exact finite-depth formulation and substantially clarifies the mathematical status and scope of the persistence interpretation. The scope remains deliberately restricted to the canonical isotropic concatenated Information-Causality/random-access-code setting. No claim is made that the construction independently characterizes the full quantum correlation set.
This version substantially revises and extends the March 2026 preprints on persistence under Information Causality. The manuscript reformulates the analysis around the exact information score of the canonical concatenated binary random-access-code protocol and develops an exact positive-series representation that leads to rigorous finite-depth bounds. These results establish a complete subcritical, critical, and supercritical classification of the concatenated Information-Causality dynamics. Correlations below the Tsirelson point exhibit asymptotic loss of accumulated information; correlations above it eventually violate Information Causality at finite depth; and the Tsirelson point is uniquely characterized by finite, nonzero asymptotic informational persistence. The new version also provides controlled finite-depth corrections at criticality, a rigorous treatment of the critical remainder, a mathematical branching generalization, a local Fisher-information interpretation of the quadratic scaling, and a universality result for smooth symmetric information-divergence measures. Numerical stability near the critical regime is treated explicitly. Compared with the March versions, the present manuscript therefore replaces the primarily asymptotic stability argument with a stronger exact finite-depth formulation and substantially clarifies the mathematical status and scope of the persistence interpretation. The scope remains deliberately restricted to the canonical isotropic concatenated Information-Causality/random-access-code setting. No claim is made that the construction independently characterizes the full quantum correlation set.
This paper introduces a foundational framework that reinterprets the position of quantum correlations within the space of possible physical theories. Rather than treating the Tsirelson bound (22) merely as a physical restriction, this work demonstrates that it emerges naturally as the unique global optimum for systems maximizing their persistence in environments of unbounded complexity. By integrating Information Causality (IC) with the Variational Principle of Persistence (VPP), we provide a unified information-geometric explanation for why quantum correlations occupy their precise position between classical and no-signaling theories. Key Contributions & Highlights: The Quantum Boundary as a Persistence Optimum: We prove that for task distributions with unbounded support, the maximum survival probability combined with informational benefit sharply isolates ρ=22 as the optimal state within the IC-constrained RAC framework. Exact Benefit–Metric Correspondence: We establish a direct identity linking the curvature of the informational benefit function to the classical Fisher information of the effective binary symmetric channel (G′′=IF/ln2). This reveals that IC is equivalent to the stability of the Fisher–Rao metric pullback under protocol concatenation, with the Tsirelson bound as the critical eigenvalue. Generalized Systemic Reduction Paradox (SRP): We identify a new optimization mechanism — a generalization of the SRP introduced in our prior VPP work — where the optimal state does not arise from classical diminishing returns (concave benefit vs. convex cost), but from a strictly convex benefit colliding with a hard viability wall, producing a corner optimum at the constraint boundary. Structural Necessity of Shannon Entropy: We demonstrate that Shannon entropy is the unique measure compatible with the concatenated RAC structure, grounded in its exclusive satisfaction of the strong chain rule. Alternatives such as Rényi entropy inherently fail to reproduce the correct quantum bounds. Significance: This manuscript bridges device-independent quantum foundations with information geometry and viability theory, offering a mathematical derivation of the Tsirelson bound as the optimal operational regime for compositional information processing under IC — within the CHSH scenario. Extensions to the full quantum correlation set remain an open question explicitly acknowledged in the paper. Reproducibility Package A reproducibility package accompanying this manuscript is available as a supplementary file. It includes a Jupyter/Colab notebook (ic_figures_colab_v3.ipynb) that reproduces Fig. 2 (Itotal vs. concatenation depth and viability horizon nmax vs. ρ) using high-precision arithmetic (mpmath, 80 decimal places) to avoid numerical cancellation near the Tsirelson point. The package also includes four CSV files containing the numerical data underlying Figs. 3–5. The notebook runs end-to-end on Google Colab with no manual configuration required.
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.
This preprint develops marginal information persistence as a framework in which information itself is treated as the dynamical variable under repeated protocol composition. The central question is which information measures vanish, remain marginally finite, or persist exactly as concatenation depth increases. For the canonical binary concatenated entanglement-assisted random access code, the complete pre-query quantum register is characterized in closed form for arbitrary primitive correlation bias. At the Tsirelson point, Bob's complete register retains exactly one bit of Holevo information about the full database at every concatenation depth, while every individual target correlation decays exponentially. The work further distinguishes information stored in the quantum register from information operationally extractable from a single copy. For the associated critical Clifford ensemble, the accessible-information problem reduces exactly to a global unit-vector optimization. Explicit finite-depth bounds show that the optimal single-copy accessible information decays exponentially with concatenation depth, even though the complete-register Holevo information remains exactly one bit. The task-summed random-access score remains finite at the same critical point because it combines mutually exclusive query contexts. Complete-register Holevo information, target marginals, task-summed random-access information, and single-copy accessible information therefore occupy distinct asymptotic classes under the same recursion. The analysis connects marginal information persistence with Information Causality, Clifford observables, Holevo information, accessible information, entropy optimization, and earlier Fisher-information formulations of criticality in concatenated protocols. It also clarifies the relation to previous work on persistence, random-access codes, and information-theoretic stability. Depth-two consequences are tested experimentally on IBM Marrakesh and Quantum Inspire Tuna-17. Both platforms yield positive 99.9% finite-shot lower confidence bounds on an implemented decoder gap. Full-register physical tomography provides separate reconstruction estimates of the corresponding strong information gap. This Zenodo record contains the main manuscript and the Supplementary Information.
Information causality is a physical principle that constrains bipartite post-quantum nonlocal correlations from information-theoretic assumptions. A direct characterization of the correlations satisfying it, however, remains difficult because the defining entropic condition must hold for all admissible protocols in the corresponding task. Here, we formulate the single-copy information causality problem as an optimization over all protocol parameters and simplify it by proving a deterministic reduction. We then show that generic adaptive multi-copy protocols can be represented as single-copy protocols applied to an effective behavior obtained by local wirings. As a consequence, for families of correlations closed under wirings, excluding single-copy violations suffices to exclude all finite-copy adaptive-protocol violations. We formulate the resulting membership and set-inclusion problems as optimization problems and discuss possible semidefinite programming relaxations. As an application, we study expansions of the information causality functional around zero-capacity channels, generalizing a method recently employed by Gachechiladze and Miklin to derive the Tsirelson--Landau--Masanes boundary from information causality. For expansions centered on channels whose output distribution has full support, imposing the second-order constraints for all single-copy protocols characterizes exactly the set of macroscopic locality in the CHSH scenario. Expanding instead around appropriate constant-output channels with perturbations that change the channel support, we show that every single-copy IC violation can be witnessed already at first order with a channel of arbitrarily small capacity.
Marginal information persistence is introduced as the condition that accumulated operational information under recursive composition approaches a finite, strictly positive asymptotic value only when the growth of available records exactly balances the loss of local distinguishability. In the canonical binary concatenated Information-Causality protocol, this criterion uniquely selects the Tsirelson bias η = 1/√2; for anisotropic coefficients, the corresponding critical set is ∑ᵢvᵢ² = 1. The exact Shannon recursion admits a positive series representation, while finite-depth corrections on the critical set are organized by the Rényi spectrum of the normalized squared coefficients, with collision entropy determining the leading correction rate. The central result concerns the physical pre-query register of the canonical singlet-based binary entanglement-assisted random access code (EARAC). For primitive bias v, the complete register satisfies the exact identity I(Aₖ:Rₖ) = G[(2v²)^(k/2)], whereas each target marginal satisfies I(Aⱼ:Rₖ) = G(vᵏ). At the critical value v = 1/√2, every individual target correlation vanishes exponentially with depth, while the mutual information between the complete database and the complete pre-query register remains exactly one bit at every depth. The difference between complete-register information and the sum of target marginals is resolved exactly as a sum of conditional mutual informations. The result therefore provides an exactly solvable example of marginal attenuation coexisting with depth-independent global information persistence in a concatenated quantum register. Two direct depth-two experiments on IBM ibm_marrakesh test this separation. A 128-circuit witness experiment yields the nonasymptotic certificate I(A₂:R₂) − ΣⱼI(Aⱼ:Yⱼ) ≥ 0.013245941 bit at 99.9% confidence, under explicitly stated repeated-shot, static-branch, and intended-observable assumptions. A second 864-circuit experiment performs full three-qubit tomography of the pre-query register. Physical maximum-likelihood reconstruction gives I(A₂:R₂) = 0.691632483 bit, ΣⱼI(Aⱼ:R₂) = 0.535829616 bit, and a reconstructed strong gap of 0.155802867 bit; an independent linear-inversion/PSD reconstruction agrees to within 4.06×10⁻⁴ bit. Bootstrap and matched-shot null simulations are reported only as estimator diagnostics; no strictly positive state-space confidence bound is claimed for the tomographic strong gap. The complete-register theorem motivates a quantum-information-processing perspective in which target-by-target readout can underestimate information retained by a composite quantum register. Connections to collective readout, information scrambling, quantum data hiding, and quantum error correction are discussed as related but distinct research directions. No computational speedup, fault-tolerance theorem, universal collective decoder, or characterization of the full quantum correlation set is claimed. This Zenodo record includes the manuscript together with the reproducibility package for the reported hardware analyses, including experimental data, reconstruction outputs, analysis scripts, and integrity checks.
Information causality (IC) was one of the first principles that have been invoked to bound the set of quantum correlations. For some families of correlations, this principle recovers exactly the boundary of the quantum set; for others, there is still a gap. We close some of these gaps using a new quantifier for IC, based on the notion of ``redundant information''. This progress was made possible by the recognition that the principle of IC can be captured without referring to the success criterion of random access codes. We give strong numerical evidence that the new definition is still obeyed by quantum correlations in the same scenario.