Why do correlations between the results of measurements performed on physical systems violate Bell and non-contextuality inequalities up to some specific limits? The answer may follow from the observation that in quantum theory, unlike in other theories, whenever there is an experiment to measure $A$ simultaneously with $B$, another to measure $B$ with $C$, and another to measure $A$ with $C$, there is always an experiment to measure all of them simultaneously. This property implies that quantum theory satisfies a seemingly irrelevant restriction called the exclusivity (E) principle which, surprisingly, explains the set of quantum correlations in some fundamental scenarios. An open problem is whether the E principle explains the maximum quantum violation of the Bell-CHSH inequality. Here we show experimentally that the E principle imposes an upper bound to the violation of the Bell-CHSH inequality that matches the maximum predicted by quantum theory. For that, we use the result of an independent experiment testing a specific non-contextuality inequality. We perform both experiments: the Bell-CHSH inequality experiment on polarization entangled states of pairs of photons in Stockholm and, to demonstrate independence, the non-contextuality inequality experiment on single photons' orbital angular momentum states in Rome. The observed results provide the first experimental evidence that the E principle determines the limits of quantum correlations and prove that hypothetical super-quantum violations for either experiment would violate the E principle. This supports the conclusion that the E principle captures a fundamental limitation of nature. If this is true, much of quantum theory trivially follow from merely taking the E principle to be a fundamental truth, and various information-theoretic postulates are also simplified and/or strengthened.
Why do correlations between the results of measurements performed on physical systems violate Bell and non-contextuality inequalities up to some specific limits? The answer may follow from the observation that in quantum theory, unlike in other theories, whenever there is an experiment to measure A simultaneously with B, another to measure B with C, and another to measure A with C, there is always an experiment to measure all of them simultaneously. This property implies that quantum theory satisfies a seemingly irrelevant restriction called the exclusivity (E) principle which, surprisingly, explains the set of quantum correlations in some fundamental scenarios. An open problem is whether the E principle explains the maximum quantum violation of the Bell-CHSH inequality. Here we show experimentally that the E principle imposes an upper bound to the violation of the Bell-CHSH inequality that matches the maximum predicted by quantum theory. For that, we use the result of an independent experiment testing a specific non-contextuality inequality. We perform both experiments: the Bell-CHSH inequality experiment on polarization entangled states of pairs of photons in Stockholm and, to demonstrate independence, the non-contextuality inequality experiment on single photons' orbital angular momentum states in Rome. The observed results provide the first experimental evidence that the E principle determines the limits of quantum correlations and prove that hypothetical super-quantum violations for either experiment would violate the E principle. This supports the conclusion that the E principle captures a fundamental limitation of nature. If this is true, much of quantum theory trivially follow from merely taking the E principle to be a fundamental truth, and various information-theoretic postulates are also simplified and/or strengthened.
Recently, many simple principles have been proposed that can explain quantum limitations on possible sets of experimental probabilities in nonlocality and contextuality experiments. However, few implications between these principles are known. Here it is shown that the lack of irreducible third-order interference (a generalization of the idea that no probabilistic interference remains unaccounted for once we have taken into account interference between pairs of slits in a n-sit experiment) implies the principle known as the E principle or consistent exclusivity (that, if each pair of a set of experimental outcomes are exclusive alternatives in some measurement, then their probabilities are consistent with the existence of a further measurement in which they are all exclusive). This is a step towards a more unified understanding of quantum nonlocality and contextuality, which promises to allow derivations of important results from minimal, easily grasped assumptions. As one example, this result implies that lack of third-order interference bounds violation of the Clauser-Horne-Shimony-Holt-Bell inequality to 2.883.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation. In particular, within the framework of a standard Bell experiment, i.e., a Bell inequality test that is directly performed on a single copy of a quantum state r, we have derived two algorithms to determine, respectively, a lower bound and an upper bound on the strength of correlations that r can offer for any given Bell inequality. Both of these algorithms make use convex optimization techniques in the form of a semidefinite program. By examples, we show that these algorithms can often be used in tandem, in conjunction with convexity arguments, to determine if a quantum state can offer nonclassical correlations and hence violates a given Bell inequality. On the other hand, since a standard Bell experiment typically involves measurements over many copies of the quantum systems, we have also investigated the possibility of enhancing the strength of nonclassical correlation by, instead, performing collective measurements on multiple copies of the quantum systems. Our findings show that even without postselection, such joint measurements may also lead to stronger nonclassical correlations, and hence a better Bell inequality violation. Meanwhile, previous studies have indicated that entangled state admitting locally causal models may still lead to observable nonclassical correlations if, prior to a standard Bell experiment, the state is subjected to some appropriate local preprocessing. This phenomenon of hidden nonlocality was discovered more than a decade ago, but to date, it is still not known if all entangled states can demonstrate nonclassical correlations through these more sophisticated Bell experiments. A key result in this thesis then consists of showing that for all bipartite entangled states, observable nonclassical correlations, in the form of a Bell-CHSH inequality violation, can indeed be derived if we allow both local preprocessing and the usage of shared ancillary state which by itself does not violate the Bell-CHSH inequality. This establishes a kind of equivalence between bipartite entanglement and states that cannot be simulated by classical correlations. In summary, for a standard Bell experiment where no local preprocessing on a quantum state r is allowed, we have provided two algorithms that can be used in tandem to determine if r can be simulated by a locally causal theory, whereas in the scenario where local preprocessing is allowed, we have demonstrated that bipartite entangled states are precisely those which cannot always be simulated classically.
The view that non-classical phenomena are witnessed when noncontextuality inequalities are violated by quantum correlations has become widespread over the last decades, and many authors describe contextuality as a counter-intuitive and non-classical feature of quantum systems. In this paper we show that a classical input/output device generating contextual data (i.e., data violating noncontextuality inequalities) can easily be found if the following conditions are satisfied: (1) We only have access to a specific collection of epistemic measurements, namely measurements which do not necessarily reveal properties possessed by the system to the agent, and (2) not all these measurements can be jointly performed. The conclusion we draw from this example is twofold. Firstly, regarding model-independent contextuality, it suggests that, unlike Bell inequalities (whose violation allegedly implies non-locality), noncontextuality inequalities have no phenomenological significance per se: we cannot treat experiments as black-boxes and draw conclusions about the phenomenological status of their underlying structure based only on contextuality analysis of the data they generate. Secondly, regarding quantum theory, it indicates that one who accepts, as many interpretations suggest, that quantum theory satisfies both these conditions should not take for granted that quantum contextuality is a signature of non-classicality.
The most promising candidate for being the fundamental principle of quantum contextuality is the Exclusivity principle, which states that the sum of the probabilities of a set of pairwise exclusive events cannot exceed 1. By itself, the Exclusivity principle singles out the maximum quantum value for some important Bell and noncontextuality inequalities. We can get better results if we apply the E principle to more sophisticated scenarios. This happens because this principle exhibits activation effects: a distribution satisfying this principles does not necessarily satisfy it when combined with other distributions. Activation effects can be used to prove that the Exclusivity principle singles out the set of quantum distributions for the most simple noncontextuality inequality. It is still not known if the exclusivity principle solves the problem of explaining quantum contextuality completely, but many results have been proven that support the conjecture that it might. The main purpose of this thesis is to discuss in detail the situations in which the E principle can be used to rule out distributions outside the quantum set.
Quantum nonlocality is presented often as the most remarkable and inexplicable phenomenon known to modern science. It has been known already for a long time that the probabilistic models used to prove Bell and Clauser-Horn-Shimony-Holt inequalities (BI-CHSH) for spin polarization correlation experiments (SPCE) are incompatible with the experimental protocols of SPCE. In particular these models use the same common probability space, joint probability distributions and/or conditional independence to describe coincidence experiments in incompatible experimental settings. Strangely enough these results are not known or simply neglected. This is why we will once again reanalyze Bell locality assumptions and show that they have nothing to do with the notion of Einsteinian locality therefore their violation should not be called quantum nonlocality but rather quantum non-Kolmogorovness or quantum contextuality. Moreover if local variables describing the measuring instruments are correctly taken into account then BI-CHSH can no longer be proven and one can easily construct non-signaling probabilistic models able to reproduce the predictions of QT. The violation of BI-CHSH is considered usually as a proof that a quantum state is entangled. Since BI-CHSH are violated also in some experiments from outside the domain of quantum physics therefore the entanglement is not exclusively a quantum phenomenon. In order to further demystify these notions we show that one can prepare two macroscopic systems in such a way that simple realizable local experiments on these systems violate BI. In view of these arguments the further testing of BI-CHSH inequalities in search for the loopholes does not seem to be necessary.
The free will theorem states that if experimenters have free will in the sense that their choices are not a function of the past, so must some elementary particles. The theorem goes beyond Bell's theorem as it connects the two fundamental resources behind quantum technologies: single-particle contextuality, which supplies the power for quantum computation, and two-particle non-locality, which allows for quantum secure communication. The theorem relies on three axioms: (i) There is a maximum speed for propagation of information, (ii) single particles can exhibit contextuality, (iii) two separated particles can exhibit Einstein-Podolsky-Rosen (EPR) correlations. Here we report the first experimental test of the free will theorem. We used pairs of hyper-entangled photons entangled in path and polarization and enforced the conditions for invoking axiom (i) by measuring each photon in a different laboratory. We certified axiom (ii) by testing the violation of the Peres-Mermin non-contextuality inequality and axiom (iii) by showing EPR correlations between the two laboratories. The three axioms imply an upper bound on the sum of the correlations among the outcomes of sequential measurements in the same laboratory and the correlations between the outcomes in both laboratories. We observed a violation of this bound by more than 66 standard deviations. This reveals that quantum non-locality can be produced when single-particle contextuality is combined with correlations which are not non-local by themselves. Our results demonstrate the resources needed for quantum computation and quantum secure communication simultaneously in the same experiment and open the door to quantum machines that efficiently achieve both tasks.