We prove that quantum mechanics is the unique optimal physical theory under Information Causality (IC): it is the only rotationally covariant bipartite correlation theory that both respects IC and maximises non-local coordination. Concretely, among all IC-admissible positive semi-definite (PSD) kernels E(d) = −∑ₗ≥₁ aₗPₗ(cos d) with aₗ ≥ 0, the quantum correlation E(d) = −cos d is the unique maximiser of the CHSH value. The proof combines the Eigenvector Protocol (IC implies aₗ ≥ 0) with the Tsirelson uniqueness result into a single optimality statement. No second independent axiom is required: Tsirelson saturation is not an additional assumption but a consequence of optimality under IC. This provides the tightest known single-principle characterisation of quantum correlations, establishing that quantum mechanics is not merely consistent with IC — it is the optimal realisation of IC.
We prove that quantum mechanics is the unique optimal physical theory under Information Causality (IC): it is the only rotationally covariant bipartite correlation theory that both respects IC and maximises non-local coordination. Concretely, among all IC-admissible positive semi-definite (PSD) kernels E(d) = −∑ₗ≥₁ aₗPₗ(cos d) with aₗ ≥ 0, the quantum correlation E(d) = −cos d is the unique maximiser of the CHSH value. The proof combines the Eigenvector Protocol (IC implies aₗ ≥ 0) with the Tsirelson uniqueness result into a single optimality statement. No second independent axiom is required: Tsirelson saturation is not an additional assumption but a consequence of optimality under IC. This provides the tightest known single-principle characterisation of quantum correlations, establishing that quantum mechanics is not merely consistent with IC — it is the optimal realisation of IC.
This work presents a complete, non-circular, and principle-based derivation of the quantum correlation law E(Δθ)=−cos(Δθ) from three operational postulates: no-signaling with fair marginals, rotational covariance, and Information Causality (IC). The central contribution is the proof that IC alone enforces the kernel positivity (positive semidefiniteness) of the correlation matrix K(θ,ϕ)=−E(θ−ϕ). This closes a long-standing axiomatic gap, as prior derivations often required kernel positivity as an independent mathematical assumption.Combined with the Herglotz theorem and Tsirelson saturation, this yields the unique harmonic form of the cosine law without additional ad-hoc postulates. Furthermore, numerical analysis of the hyperbolic extension (SO(2,1)) reveals that while IC still implies kernel positivity in non-Euclidean geometries, the Tsirelson bound can be exceeded. This suggests a deep interplay between spacetime geometry and the observed limits of quantum correlations.
Information causality (IC) was introduced as a physical principle constraining correlations in non-signaling theories. Whether it can recover the exact quantum correlation boundary, beyond Uffink's inequality, has remained an open question. Here, we combine its generalized formulation for correlated inputs with a new communication protocol to derive quantum Bell inequalities that exactly characterize the quantum correlations in the simplest bipartite Bell scenario, with two binary measurements. In particular, we derive the Tsirelson-Landau-Masanes criterion directly from IC. Thus, the generalized IC implies macroscopic locality, while we also present macroscopically local correlations that violate the generalized IC. This establishes that generalized IC is a strictly stronger principle in this scenario. Together with our earlier result that generalized IC implies a nontrivial communication complexity principle, these findings strengthen the role of information causality in explaining the limits of quantum nonlocality and provide a systematic route to deriving tighter bounds on the set of quantum correlations in more general Bell scenarios.
Information causality (IC) was introduced as a physical principle that imposes constraints on the non-local correlations between two parties (Alice and Bob) in a Bell scenario. Specifically, it states that the information that Bob can gain about an n-bit database held by Alice is bounded by the information she communicates to him. To date, the question whether IC for any n∈N singles out the set of quantum correlations remains open, meaning that it is unknown whether for any number of inputs m and outputs d of the two parties the set of correlations that satisfy IC exactly coincides with the quantum correlations. In this work, we answer this question in the negative. Firstly, we show that for any finite database length n≥2, there is a bipartite set of correlations that satisfies IC for all compatible protocols and that exhibits post-quantum correlations in the Bell scenario with n+1 inputs and 2 outcomes per party. This result relies on constructing an entropic proof of IC for GPTs that may be of independent interest. We further show that in the Bell scenario with n+1 inputs and 2 outcomes per party, our constructed sets of correlations lead to neither a superset nor a subset of the quantum correlations. Secondly, we construct a set of correlations in the Bell scenario with 3 inputs and 2 outputs per party that satisfies IC (for all database sizes n∈N) and that includes post-quantum points. Consequently, all known formulations of information causality fail to fully characterize the bipartite set of quantum correlations, already in the 3-input, 2-outcome Bell scenario.
The Information Causality principle was proposed to re-derive the Tsirelson bound, an upper limit on the strength of quantum correlations, and has been suggested as a candidate law of nature. The principle states that the Shannon information about Alice’s distant database gained by Bob after receiving an m bit message cannot exceed m bits, even when Alice and Bob share non-local resources. As originally formulated, it can be shown that the principle is violated exactly when the strength of the shared correlations exceeds the Tsirelson bound. However, we demonstrate here that when an alternative measure of information, one of the Renyi measures, is chosen, the Information Causality principle no longer arrives at the correct value for the Tsirelson bound. We argue that neither the assumption of particular ‘intuitive’ properties of uncertainties measures, nor pragmatic choices about how to optimise costs associated with communication, are sufficient to motivate uniquely the choice of the Shannon measure from amongst the more general Renyi measures. We conclude that the dependence of the success of Information Causality on mere convention undermines its claimed significance as a foundational principle.
This review critically examines Daniel Süß's March 2026 preprint, which advances a principle-based reconstruction of quantum bipartite binary correlations. By proving that the Information Causality (IC) principle alone implies kernel positivity (positive semidefiniteness of the correlation matrix), Süß eliminates a long-standing ad-hoc assumption in prior axiomatic derivations. Combined with no-signaling, rotational covariance, and the Herglotz theorem, this yields the unique quantum correlation function E(Δθ) = −cos(Δθ) purely from operational postulates. The work further derives the maximum-entropy joint probability distribution and extends the framework to hyperbolic geometry SO(2,1), revealing that while IC still enforces positivity, the Tsirelson bound can be exceeded. This review synthesises the paper's postulates, proofs, and results; provides algebraic and geometric interpretations; surveys related literature in information-theoretic reconstructions of quantum mechanics; and discusses implications, limitations, experimental prospects, and future directions. The analysis affirms the novelty and rigor of the derivation while highlighting its deeper connection between information theory, correlation structure, and spacetime geometry. Mamun, SM (2026)……………………………..1 A Comprehensive Review of "Information Causality as the Sole Origin of the Quantum Correlation Law" by Daniel Süß (Vol-I) Closing the Axiomatic Gap in Operational Derivations of Quantum Correlations Also available on Academia.edu: https://www.academia.edu/attachments/132230261/download_file?s=portfolio
Information causality (IC) posits that communicating m classical bits cannot give the receiver access to more than m bits of information about the sender's independent data. Although IC holds in quantum theory and excludes a broad class of supra-quantum correlations, its validity for the almost-quantum set has remained open. This semidefinite relaxation of the quantum set satisfies nontrivial communication complexity, no advantage for non-local computation, macroscopic locality, local orthogonality, and numerical evidence has suggested that it may also satisfy IC. Here we show that almost-quantum correlations violate IC, and do so without bound. Unlike earlier violations of IC, which rely on biased guesses, ours is driven by zero-error certificates: each is rare but never wrong, carries information linear in its probability, and vouches for many of the sender's bits at once. This establishes a sharp dichotomy: either IC is a valid physical principle that excludes these correlations, or any nonsignalling theory realizing them admits no mutual information obeying consistency, data processing and the chain rule. In the latter case, we discuss why the chain rule is the natural property to relinquish, and how this possibility relates to histories-based formulations and to locality defined relative to the state rather than presupposed in a fixed spacetime.