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.
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.
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) 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.
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.
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.
Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in the Bell experiment. In the same work, information causality was famously shown to imply the Uffink inequality that approximates the set of quantum correlations and rederives Tsirelson's bound of the Clauser-Horne-Shimony-Holt inequality. This result found limited generalizations due to the difficulty of deducing implications of the information causality principle on the set of nonlocal correlations. In this Letter, we present a simple technique for obtaining polynomial inequalities from information causality bounding the set of physical correlations in any bipartite Bell scenario. This result makes information causality an efficient tool for approximating the set of quantum correlations. To demonstrate our method, we derive a family of inequalities which nontrivially constrains the set of nonlocal correlations in Bell scenarios with binary outcomes and equal number of measurement settings. Finally, we propose an improved statement of the information causality principle and obtain a tighter constraint for the simplest Bell scenario that goes beyond the Uffink inequality and recovers a part of the boundary of the quantum set.
The no-signalling principle lies at the heart of Bell-type experiments involving spacelike-separated parties. Although not all no-signalling correlations can be realized within quantum theory, the no-sinalling principle itself remains fundamental even for post-quantum theories, since its violation would imply superluminal signalling. In the spirit of device independent nature of the Bell inequalities, there has recently been growing interest in causal inequalities, which identify correlations admitting no causal explanation. Such correlations have been rigorously studied within the process-matrix formalism, which is built upon a constraint analogous to spacelike separation in Bell scenarios. We refer to this constraint as the single-interaction constraint, whereby each party interacts with the environment only once. Despite considerable effort, no fundamental guiding principle is currently known that characterizes the restrictions this constraint imposes on the correlations generated by Process Matrices. In this work, we address this gap by proposing a generalized causality principle for the bipartite case. We show that for certain cases, the generalised causality principle defines a strict subset of the set of all signalling correlations. This principle thus provides a fundamental limit on quantum and even post-quantum theories subject to the single-interaction constraint. By analogy with no-signalling, whose violation excludes certain causal structures among the parties, a violation of the generalised causality principle rules out a corresponding class of causal structures(causal structures with the single interaction constraint). More broadly, our techniques provide a general framework for deriving generalised causal constraints, applicable to a wide class of indefinite-causal-order scenarios.