Let NS_2,2,2 denote the nonsignalling conditional distributions P(a,b| x,y) with a,b,x,y∈0,1, and let Q_2,2,2 denote the quantum-correlation set, consisting of those distributions for which there exist a bipartite quantum state rho and binary measurements M^a_x_a=0^1, N^b_y_b=0^1 such that P(a,b| x,y)=operatornameTr!(rho(M^a_x otimes N^b_y)). Determine whether the correlations satisfying generalized information causality with correlated inputs are exactly the quantum correlations; equivalently, determine whether IC_gen=Q_2,2,2, where IC_gen⊆NS_2,2,2 is the set allowed by generalized information causality.

Information causality characterization problem

Let $\mathcal{NS}_{2,2,2}$ denote the nonsignalling conditional distributions $P(a,b\mid x,y)$ with $a,b,x,y\in\{0,1\}$ , and let $\mathcal{Q}_{2,2,2}$ denote the quantum-correlation set, consisting of those distributions for which there exist a bipartite quantum state $\rho$ and binary measurements $\{M^a_x\}_{a=0}^1$ , $\{N^b_y\}_{b=0}^1$ such that $P(a,b\mid x,y)=\operatorname{Tr}\!\left(\rho(M^a_x\otimes N^b_y)\right)$ . Determine whether the correlations satisfying generalized information causality with correlated inputs are exactly the quantum correlations; equivalently, determine whether $\mathcal{IC}_{\mathrm{gen}}=\mathcal{Q}_{2,2,2}$ , where $\mathcal{IC}_{\mathrm{gen}}\subseteq\mathcal{NS}_{2,2,2}$ is the set allowed by generalized information causality.

References

Primary source

arXiv

Additional references

Information Causality Characterizes the Set of Quantum Correlations in the Simplest Bell Scenario — arXiv

bell-inequalities foundations-of-quantum-mechanics quantum-information

Posted 3 weeks ago · edited 4 hours ago

Progress summary

Refreshed 4 hours ago

Claimed solved

A September 2026 preprint claims that generalized information causality exactly identifies quantum correlations in the simplest Bell experiment, but this claim remains unverified.

The problem asks whether generalized information causality with correlated inputs gives exactly the quantum set in the binary two-input Bell scenario, namely $\mathcal{IC}_{\mathrm{gen}}=\mathcal{Q}_{2,2,2}$ . On September 9, 2026, Mariami Gachechiladze and Nikolai Miklin claimed this equality by deriving the Tsirelson–Landau–Masanes criterion.

Known results

Correlated-input information causality produced inequalities stronger than Uffink’s inequality in the $2222$ scenario (2023), but not equality.
Information causality was compared with macroscopic locality, yielding approximation results rather than a full characterization (2021).
Numerical studies recovered portions of the quantum boundary while leaving gaps (2022–2023).

September 9, 2026 claimed characterization

The preprint states that a new correlated-input protocol derives the relevant TLM inequalities and that generalized information causality therefore exactly characterizes $\mathcal{Q}_{2,2,2}$ . It also claims generalized information causality is stronger than macroscopic locality. These are unverified claims rather than an independently established resolution.

Current status (as of October 2026): The equality $\mathcal{IC}_{\mathrm{gen}}=\mathcal{Q}_{2,2,2}$ is claimed in a September 2026 preprint, but the claim remains unverified.

Sources

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