Besides being one of the most puzzling aspects of quantum information theory, non-locality has been recognised as a valuable resource for various cryptographic protocols. We study the phenomenon of distillation of non-locality, which is the ability to generate a stronger instance of non-locality from weaker ones. We construct an eavesdropping third party who gains knowledge about the outputs of distillation protocols. This knowledge directly implies an upper bound on the degree of non-locality of the output of the protocol.
Besides being one of the most puzzling aspects of quantum information theory, non-locality has been recognised as a valuable resource for various cryptographic protocols. We study the phenomenon of distillation of non-locality, which is the ability to generate a stronger instance of non-locality from weaker ones. We construct an eavesdropping third party who gains knowledge about the outputs of distillation protocols. This knowledge directly implies an upper bound on the degree of non-locality of the output of the protocol.
The phenomenon of nonlocality, which can arise when entangled quantum systems are suitably measured, is perhaps one of the most puzzling features of quantum theory to the philosophical mind. It implies that these measurement statistics cannot be explained by hidden variables, as requested by Einstein, and it thus suggests that our universe may not be, in principle, a well-determined entity where the uncertainty we perceive in physical observations stems only from our lack of knowledge of the whole. Besides its philosophical impact, nonlocality is also a resource for information- theoretic tasks since it implies secrecy: If nonlocality limits the predictive power that any hidden variable (in the universe) can have about some observations, then it limits in particular the predictive power of a hidden variable held by an adversary in a cryptographic scenario. We investigate whether nonlocality alone can empower two parties to perform unconditionally secure communication in a feasible manner when only a provably minimal set of assumptions are made for such a task to be possible — independently of the validity of any physical theory (such as quantum theory). Nonlocality has also been of interest in the study of foundations of quantum theory and the principles that stand beyond its mathematical formalism. In an attempt to single out quantum theory within a broader set of theories, the study of nonlocality may help to point out intuitive principles that distinguish it from the rest. In theories where the limits by which quantum theory constrains the strength of nonlocality are surpassed, many “principles” on which an information theorist would rely on are shattered — one example is the hierarchy of communication complexity as the latter becomes completely trivial once a certain degree of nonlocality is overstepped. In order to study the structure of such super-quantum theories — beyond their aforementioned secrecy aspects — we investigate the phenomenon of distillation of nonlocality, the ability to distill stronger forms of nonlocality from weaker ones. By exploiting the inherent connection between nonlocality and secrecy, we provide a novel way of deriving bounds on nonlocality-distillation protocols through an ad versarial view to the problem.
Non-local correlations are not only a fascinating feature of quantum theory, but an interesting resource for information processing, for instance in communication-complexity theory or cryptography. An important question in this context is whether the resource can be distilled: Given a large amount of weak non-local correlations, is there a method to obtain strong non-locality using local operations and shared randomness? We partly answer this question by no: CHSH-type non-locality, the only possible non-locality of binary systems, which is not super-strong, but achievable by measurements on certain quantum states, has at best very limited distillability by any non-interactive classical method. This strongly extends and generalizes what was previously known, namely that there are two limits that cannot be overstepped: The Bell and Tsirelson bounds. Moreover, our results imply that there must be an infinite number of such bounds. A noticeable feature of our proof of this purely classical statement is that it is quantum mechanical in the sense that (both novel and known) facts from quantum theory are used in a crucial way to obtain the claimed results. One of these results, of independent interest, is that certain mixed entangled states cannot be distilled without communication. Weaker statements, namely limited distillability, have been known for Werner states.
Quantum theory puts forward phenomena unexplainable by classical physics - or information, for that matter. A prominent example is non-locality. Non-local correlations cannot be explained, in classical terms, by shared information but only by communication. On the other hand, the phenomenon does not allow for (potentially faster-than-light) message transmission. The fact that some non-local and non-signaling correlations are predicted by quantum theory, whereas others fail to be, asks for a criterion, as simple as possible, that characterizes which joint input-output behaviors are ``quantum'' and which are not. In the context of the derivation of such criteria, it is of central importance to understand when non-local correlations can be amplified by a non-interactive protocol, i.e., whether some types of weak non-locality can be distilled into stronger by local operations. Since it has been recognized that the searched-for criteria must inherently be multi-partite, the question of distillation, extensively studied and understood two-party scenarios, should be adressed in the multi-user setting, where much less is known. Considering the space of intrinsically n-partite correlations, we show the possibility of distilling weak non-local boxes to the algebraically maximal ones without any communication. Our protocols improve on previously known methods which still required partial communication. The price we have to pay for dropping the need for communication entirely is the assumption of permutation invariance: Any correlation that can be realized between some set of players is possible between any such set. This assumption is very natural since the laws of physics are invariant under spacial translation.
Quantum theory puts forward phenomena beyond the explanatory power of classical physics-or information, for that matter. A prominent example is non-locality. Non-local correlations cannot explained, in classical terms, by shared information but only by communication. On the other hand, the phenomenon does not allow for (potentially faster-than-light) message transmission. The fact that some non-local and non-signaling correlations are predicted by quantum theory, whereas others fail to be, asks for a criterion, as simple as possible, that characterizes which joint input-output behaviors are “quantum” and which are not. In the context of the derivation of such criteria, it is of central importance to understand when non-local correlations can be amplified by a non-interactive protocol, i.e., whether some types of weak non-locality can be distilled into stronger by local operations. Since it has been recognized that the searched-for criteria must inherently be multi-partite, the question of distillation, extensively studied and understood two-party scenarios, should be adressed in the multi-user setting, where much less is known. Considering the space of intrinsically n-partite correlations, we show the possibility of distilling weak non-local boxes to the algebraically maximal ones without any communication. Our protocols improve on previously known methods which still required partial communication. The price we have to pay for dropping the need for communication entirely is the assumption of permutation invariance: Any correlation that can be realized between some set of players is possible between any such set. This assumption is natural since the laws of physics are invariant under spacial translation.
In quantum mechanics some spatially separated sub-systems behave as if they are part of a single system, the superposition of states of this single system cannot be written as products of states of individual sub-systems,we say that the state of such system is entangled, such systems give rise to non-local correlations between outcomes of measurements. The non-local correlations are conditional probability distributions of some measurement outcomes given some measurement settings and cannot be explained by shared information.These correlations can be studied using a non-local box(NLB) which can be viewed as a quantum systema. A NLB is an abstract object which has number of inputs(measurement settings) and number of outputs(outcomes), such NLBs can be both quantum and super-quantum. The correlations are of use in quantum information theory, the stronger the correlations the more useful they are, hence we study protocols that have multiple weaker non-local systems, application of these protocols to weaker systems may result in stronger non-local correlations, we call such protocols non-locality distillation protocols. In our work here we present non-locality distillation protocols for tripartite NLBs specifically GHZ box and class 44,45 and 46 of no-signalling polytope.
Non-local correlations are one of the most fascinating consequences of quantum physics from the point of view of information: Such correlations, although not allowing for signaling, are unexplainable by pre-shared information. The correlations have applications in cryptography, communication complexity, and sit at the very heart of many attempts of understanding quantum theory - and its limits - better in terms of classical information. In these contexts, the question is crucial whether such correlations can be distilled, i.e., whether weak correlations can be used for generating (a smaller amount of) stronger. Whereas the question has been studied quite extensively for bipartite correlations (yielding both pessimistic and optimistic results), only little is known in the multi-partite case. We show that a natural generalization of the well-known Popsecu-Rohrlich box can be distilled, by an adaptive protocol, to the algebraic maximum. We use this result further to show that a much bigger class of correlations, including all purely three-partite correlations, can be distilled from arbitrarily weak to maximal strength with partial communication, i.e., using only a subset of the channels required for the creation of the same correlation from scratch. In other words, we show that arbitrarily weak non-local correlations can have a “communication value” in the context of the generation of maximal non-locality.