Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial resource behind various models of quantum computation. The practical and fundamental aspects of these non-classical resources are still poorly understood despite decades of research. We explore non-classical correlations exhibited by some of these quantum as well as super-quantum resources in the n-cycle setting. In particular, we focus on correlations manifested by Kochen–Specker–Klyachko box (KS box), scenarios involving n-cycle non-contextuality inequalities and Popescu–Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary n dimension. The non-contextuality inequalities are analysed for n-cycle setting, and the condition for the quantum violation for odd as well as even n-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the phase space case. Furthermore, we simulate a generalised PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. Our work connects generalised PR boxes, arbitrary dimensional KS boxes, and n-cycle non-contextuality inequalities and thus provides the pathway for the study of these contextual and nonlocal resources at their junction.
Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial resource behind various models of quantum computation. The practical and fundamental aspects of these non-classical resources are still poorly understood despite decades of research. We explore non-classical correlations exhibited by some of these quantum as well as super-quantum resources in the n-cycle setting. In particular, we focus on correlations manifested by Kochen–Specker–Klyachko box (KS box), scenarios involving n-cycle non-contextuality inequalities and Popescu–Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary n dimension. The non-contextuality inequalities are analysed for n-cycle setting, and the condition for the quantum violation for odd as well as even n-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the phase space case. Furthermore, we simulate a generalised PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. Our work connects generalised PR boxes, arbitrary dimensional KS boxes, and n-cycle non-contextuality inequalities and thus provides the pathway for the study of these contextual and nonlocal resources at their junction.
Abstract We define a family of ‘no signaling ’ bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining corre-lations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The mar-ginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the ‘no signaling ’ poly-tope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum re-sources for all inputs. We comment on the significance of these results for contextu-ality and nonlocality in ‘no signaling ’ theories.
Abstract The relations between Bell nonlocality and Kochen–Specker contextuality have been subject of research from many different perspectives in the last decades. Recently, some interesting results on these relations have been explored in the so-called generalized Bell scenarios, that is, scenarios where Bell spatial separation (or agency independence) coexist with (at least one of the) parties’ ability to perform compatible measurements at each round of the experiment. When this party has an n-cycle compatiblity setup, it was first claimed that Bell nonlocality could not be concomitantly observed with contextuality at this party’s local experiment. However, by a more natural reading of the definition of locality, it turns out that both Bell nonlocality and local contextuality can, in fact, be jointly present. In spite of it, in this work we prove that in the simplest of those scenarios there cannot be arbitrary amounts of both of these two resources together. That is, in these cases we show that the violation of any Bell inequality limits the possible violations of any local noncontextuality inequality. We also explore this trade-off relation using quantifiers of nonlocality and contextuality, discussing how such a relation can be understood in terms of a ‘global’ notion of contextuality, and we study possible extensions of this result to other scenarios.
Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure. Contextuality, on the other hand, is on a more controversial foundation. In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality. First, I show that Bell inequalities can be derived solely from the assumptions of no-signalling and no-fine-tuning of the causal model. This removes two extra assumptions from a recent result from Wood and Spekkens, and remarkably, does not require any assumption related to independence of measurement settings -- unlike all other derivations of Bell inequalities. I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning. Thus the quantum violation of classical causality goes beyond the case of space-like separated systems, and manifests already in scenarios involving single systems.
The assumption of local realism, in a Bell locality scenario, imposes nontrivial conditions on the Shannon entropies of the associated probability distributions, expressed by linear entropic Bell inequalities. In principle, these entropic inequalities provide necessary but not sufficient criteria for the existence of a local hidden variable model reproducing the correlations, as, for example, the paradigmatic nonlocal Popescu-Rohrlich (PR) box is entropically not different from a classically correlated box. In this paper we show that for the n-cycle scenario, entropic inequalities completely characterize the set of local correlations. In particular, every nonsignaling box which violates the Clauser-Horne-Shimony-Holt (CHSH) inequality---including the PR box---can be locally modified so that it also violates the entropic version of CHSH inequality. As we show, any nonlocal probabilistic model when appropriately mixed with a local model, violates an entropic inequality, thus evidencing a very peculiar kind of nonlocality. As the n-cycle captures equally well both the notion of local realism introduced by Bell and that of noncontextuality presented by the Kochen-Specker theorem, the results are also valid for noncontextuality scenarios.
The rapidly developing interdisciplinary field of quantum information, which merges quantum and information science, studies non-classical aspects of quantum systems. These studies are motivated by the promise that the non-classicality can be used to solve tasks more efficiently than classical methods would allow. In many quantum informational studies, non-classical behaviour is attributed to the notion of entanglement. In this thesis we use photons to experimentally investigate fundamental questions such as: What happens to the entanglement in a system when it is affected by noise? In our study of noisy entanglement we pursue the challenging task of creating bound entanglement. Bound entangled states are created through an irreversible process that requires entanglement. Once in the bound regime, entanglement cannot be distilled out through local operations assisted by classical communication. We show that it is possible to experimentally produce four-photon bound entangled states and that a violation of a Bell inequality can be achieved. Moreover, we demonstrate an entanglement-unlocking protocol by relaxing the condition of local operations. We also explore the non-classical nature of quantum mechanics in several single-photon experiments. In these experiments, we show the violation of various inequalities that were derived under the assumption of non-contextuality. Using qutrits we construct and demonstrate the simplest possible test that offers a discrepancy between classical and quantum theory. Furthermore, we perform an experiment in the spirit of the Kochen-Specker theorem to illustrate the state-independence of this theorem. Here, we investigate whether or not measurement outcomes exhibit fully contextual correlations. That is, no part of the correlations can be attributed to the non-contextual theory. Our results show that only a small part of the experimental generated correlations are amenable to a non-contextual interpretation.
Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and they are key resources for quantum advantage in information-processing tasks.Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure.Contextuality, on the other hand, is on a more controversial foundation.In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality.First, I show that Bell inequalities can be derived solely from the assumptions of no signaling and no fine-tuning of the causal model.This removes two extra assumptions from a recent result from Wood and Spekkens and, remarkably, does not require any assumption related to independence of measurement settings-unlike all other derivations of Bell inequalities.I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning.Thus, the quantum violation of classical causality goes beyond the case of spacelike-separated systems and already manifests in scenarios involving single systems.