Characterising quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It has been shown that when considered with respect to so-called locally quantum observables, bipartite non-signalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) non-signalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalisation of no-signalling in the form of no-disturbance to dilated systems. We prove that non-signalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.
Characterising quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It has been shown that when considered with respect to so-called locally quantum observables, bipartite non-signalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) non-signalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalisation of no-signalling in the form of no-disturbance to dilated systems. We prove that non-signalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.
Characterizing quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put forth by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It was shown that, when considered with respect to so-called locally quantum observables, bipartite nonsignalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) nonsignalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalization of no-signalling in the form of no-disturbance to dilated systems. We prove that nonsignalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.
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.
Bell's seminal paper shows that some correlations in quantum theory are not reconcilable with hidden variables and the classical notion of locality. Yet, a weaker notion of locality, known as no-signalling, survives the no-go-result. Here, we study its restrictiveness by considering the full set of local quantum observables. This leads to a much larger set of no-signalling constraints than usually considered, which is enough to exclude PR-boxes and other types of super-quantum correlations. We emphasise the close connection with contextuality, in particular, we show how no-signalling arises naturally from context composition. Finally, we prove a one-to-one correspondence between quantum states and collections of (non-signalling) probability distributions over product contexts under an additional consistency condition between time arrows in subsystems.
We introduce a framework in which a variety of theories can be defined that share two features with quantum mechanics: the no-signalling principle for states, and the fact that the global state of a multi-partite system can be completely specified by correlations between local measurements on the individual subsystems. The aim is to investigate the relationships between the physical properties of these theories and the information processing possibilities that each one offers. One of these theories, which we call Generalised Non-Signalling Mechanics, includes states that can give rise to arbitrary non-signalling correlations, including the super-quantum correlations that have become known in the literature as non-local machines or PR boxes. By investigating these correlations in the context of a theory with well-defined dynamics, we hope to make further progress with a question raised by Popescu and Rohrlich: why does quantum mechanics not allow these strongly non-local correlations? We show that the existence of strongly non-local correlations forces much of the dynamics in this theory to be, in a certain sense, trivial, with consequences for teleportation, cryptography and computation. We also investigate another theory, which we call Generalised Local Mechanics, since all states in this theory are local. This has its own consequences for cryptography and computation. Finally, we raise the question of what further axiom(s) could be added to our framework in order uniquely to identify quantum mechanics.
Physical theories constrained with local quantum structure and satisfying the no-signalling principle can allow beyond-quantum global states. In a standard Bell experiment, correlations obtained from any such beyond-quantum bipartite state can always be reproduced by quantum states and measurements, suggesting local quantum structure and no-signalling to be the axioms to isolate quantum correlations. In this letter, however, we show that if the Bell experiment is generalized to allow local quantum inputs, then beyond-quantum correlations can be generated by every beyond-quantum state. This gives us a way to certify beyond-quantumness of locally quantum no-signalling theories and in turn suggests requirement of additional information principles along with local quantum structure and no-signalling principle to isolate quantum correlations. More importantly, our work establishes that the additional principle(s) must be sensitive to the quantum signature of local inputs. We also generalize our results to multipartite locally quantum no-signalling theories and further analyze some interesting implications.
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.