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 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.
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.
Bell's theorem asserts that no local hidden variable theory can explain the predictions of quantum theory in an experiment where spacelike separated measurements are performed in distant laboratories. Loophole-free Bell tests performed in the last decade demonstrate Bell nonlocality as a property of Nature. However, the amount of nonlocality allowed in quantum theory is limited, compared to the sole restriction of no-signaling, meaning the impossibility of faster-than-light communication implied by special relativity. Information causality is a physical principle that generalizes no-signaling and is satisfied by quantum theory. It is based on the idea that shared quantum entanglement cannot enable a receiver to obtain more classical information than how much was sent by a distant sender. Remarkably, the principle was shown to imply the maximal quantum bound for the violation of the most well-known Bell inequality. The aim of this thesis is to widen our understanding of information causality and compare its predictions with other known outer approximations of the quantum set of correlations. We build upon the recent realization that most of the known consequences of information causality can be derived with a single copy of the shared systems, whereas before it was thought that many copies were necessary. We develop a novel optimization framework which bounds the possible violations of information causality by other sets of correlations, allowing us to certify when violations are not possible. We generalize the statement of information causality and reach a precise definition for the set of correlations satisfying this principle. We show that when searching for violations of information causality by physical theories, considering many copies is not necessary. Our aforementioned optimization framework approximates the information causality set from the outside. Conversely, we propose a different approach which allows us to approximate this set from the inside.
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.
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.
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.