How can a learned representation remain useful when the question it must answer is chosen only after encoding? Preserving information is essential, but does not by itself ensure access to the requested target. We address this problem by deriving "neural information causality (Neural-IC)," a representation law that connects causal access to the physically specified interface capacity. For a fresh database of independent bits, the aggregate information recoverable across later queries cannot exceed that capacity, even with pre-established quantum resources. A decomposition separates capacity slack, information organized jointly across targets, and losses in producing answers. Exhaustive evaluation of trained binary codes reveals why nearly full use of a memory's information budget can coexist with limited retrieval. In a nested Bell-correlation construction, quantum assistance improves average retrieval over the optimal classical one-bit benchmark within the same communicated budget. These results give representation learning a design principle that connects information capacity to the organization and extraction of target information. By locating the constraints on later answers, the framework can inform memory allocation, encoding objectives, and decoder outputs, providing a basis for seeking better retrieval within a fixed budget.
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 is a physical principle which states that the amount of randomly accessible data over a classical communication channel cannot exceed its capacity, even if the sender and the receiver have access to a source of nonlocal correlations. This principle can be used to bound the nonlocality of quantum mechanics without resorting to its full formalism, with a notable example of reproducing the Tsirelson's bound of the Clauser-Horne-Shimony-Holt inequality. Despite being promising, the latter result found little generalization to other Bell inequalities because of the limitations imposed by the process of concatenation, in which several nonsignaling resources are put together to produce tighter bounds. In this work, we show that concatenation can be successfully replaced by limits on the communication channel capacity. It allows us to rederive and, in some cases, significantly improve all the previously known results in a simpler manner and apply the information causality principle to previously unapproachable Bell scenarios.
Neural representations learned by neural networks encode task-relevant information, but their behavior under communication constraints is still poorly understood. We propose an information-theoretic framework for the comparison of classical compression and quantum-inspired amplitude encoding for the transfer of representations under controlled dimensional constraints. We analyze frozen intermediate features extracted from a pretrained ResNet-50 on the ImageNet-1K validation set at different depths in the network. The classical pipeline performs rate-controlled dimensionality reduction and uniform quantization, while the quantum-inspired pipeline does amplitude encoding and computational-basis probability decoding without variational circuits or trainable quantum parameters. Quality of representation was evaluated using differential entropy and a decoder-based lower bound on mutual information. Classical compression achieves higher decoder-based mutual information lower bounds at moderate and high communication budgets. However, the quantum-inspired pipeline retained a larger fraction of decoder-extractable task-relevant information under severe dimensional compression, with resource-normalized information efficiency providing a complementary perspective to the substantially higher absolute decoder-based mutual information lower bounds of the classical pipeline. Robustness analyses with qubit reduction and physically motivated noise models showed predictable degradation. Ablation and SHAP analyses indicate that task-relevant information is structured within representational subspaces. These findings support quantum-inspired representation transfer as a framework for studying communication-efficient neural representation transfer under low-bandwidth constraints.
Information Causality contributes to the program of deriving fundamentals of quantum theory from information theoretic principles. It puts restrictions on the amount of information learned by a party (Bob) from the other party (Alice) in a one-way communication scenario: Bob receives an index b, and after a one-way communication from Alice, tries to recover the b-th bit of Alice's input. In this manuscript we note that Information Causality is indeed a point in the dual of the Gray-Wyner region in the case where Alice's input bits are chosen independently at random. The main motivation of this work was to study this connection in the case of correlated input bits. Our approach to forge this connection was to propose a new postulate called Accessibility of Mutual Information (AMI) on the underling physical theory. This approach, explained in the first version of this paper, fails since AMI is not satisfied by the quantum theory.
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.