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.
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.
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 paper, we present a simple technique for obtaining polynomial inequalities from information causality, bounding the set of physical correlations in any Bell scenario. To demonstrate our method, we derive a family of inequalities which non-trivially 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, obtain tighter constraints for the simplest Bell scenario that goes beyond the Uffink inequality, and recovers a part of the boundary of the quantum set.
Information causality states that the information obtainable by a receiver cannot be greater than the communication bits from a sender, even if they utilize no-signaling resources. This physical principle successfully explains some boundaries between quantum and postquantum nonlocal correlations, where the obtainable information reaches the maximum limit. We show that no-signaling resources of pure partially entangled states produce randomness (or noise) in the communication bits, and achievement of the maximum limit is impossible, i.e., the information causality principle is insufficient for the full identification of the quantum boundaries already for bipartite settings. The nonlocality inequalities such as so-called the Tsirelson inequality are extended to show how such randomness affects the strength of nonlocal correlations. As a result, a relation followed by most of quantum correlations in the simplest Bell scenario is revealed. The extended inequalities reflect the cryptographic principle such that a completely scrambled message cannot carry information.
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.
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.
Quantum mechanics has been a paradigm shift and a revolutionary framework in our understanding of the physical world. The theory has been able to describe a wide variety of phenomena and has been experimentally verified with great precision. Despite that, to this day, the seemingly ad hoc formulation of quantum theory and several of its features still elude an intuitive understanding. At the same time, the applications of quantum mechanics in information theory have emerged as a promising avenue. Namely, its potential advantages in computation, in the so-called nascent field of quantum computation and in communication and information processing tasks such as quantum teleportation and super-dense coding. In all these endeavours, a significant effort has been made in understanding the maximum extent to which quantum mechanics can provide an advantage. This thesis explores an intersection of these two research lines, i.e. to have a physical explanation of some of the features of quantum mechanics and at the same time, study the outer limits of quantum mechanics. The combining insight rests on a newer foundational idea: that information itself is physical rather than an abstract entity and thus, is subject to physical laws. In this thesis, we explore the principle of information causality, which states that in any communication scenario, the amount of information carried is bounded by the degrees of freedom of the carrier. Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in a Bell scenario, which is a communication scenario involving multiple parties with access to a shared randomness resource. This principle has been proposed to recover some of the well-known features of quantum mechanics, specifically Tsirelson’s bound of the Clauser-Horne-Shimony-Holt inequality. Earlier results found limited generalisations due to the difficulty of deducing implications of the information causality principle. In this thesis, we greatly expand the scope of applicability of the principle. We develop a general-purpose algorithm to derive constraints on the set of quantum correlations. We extend the principle to be applicable to a wider variety of Bell scenarios, derive new families of quantum Bell inequalities and prove new bounds on the success probabilities of Entanglement Assisted Random Access Codes. We introduce an extension of the principle which applies to any distributed computing scenario. Using this extension, we improve on several previously known results in the field, and in certain cases, we even recover part of the quantum set as well. This extension provides rich insights into the communication complexity of distributed functions, using which we prove theory-independent randomised communication complexity bounds for several well-known functions and provide another general-purpose algorithm to bound the randomised quantum communication complexity of any function. As a consequence of the extension, we also establish that the extension supersedes the principle of non-trivial communication complexity.