Browsing by Author "Cunha, Marcelo de Oliveira Terra"

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    Exclusivity principle forbids sets of correlations larger than the quantum set.
    (2014) Amaral, Barbara; Cunha, Marcelo de Oliveira Terra; Cabello Quintero, Adán
    We show that the exclusivity (E) principle singles out the set of quantum correlations associated with any exclusivity graph assuming the set of quantum correlations for the complementary graph. Moreover, we prove that, for self-complementary graphs, the E principle, by itself (i.e., without further assumptions), excludes any set of correlations strictly larger than the quantum set. Finally, we prove that, for vertex-transitive graphs, the E principle singles out the maximum value for the quantum correlations assuming only the quantum maximum for the complementary graph. This opens the door for testing the impossibility of higher-than-quantum correlations in experiments.
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    Noncontextual wirings.
    (2018) Amaral, Barbara Lopes; Cabello Quintero, Adán; Cunha, Marcelo de Oliveira Terra; Aolita, Leandro
    Contextuality is a fundamental feature of quantum theory necessary for certain models of quantum computation and communication. Serious steps have therefore been taken towards a formal framework for contextuality as an operational resource. However, the main ingredient of a resource theory—a concrete, explicit form of free operations of contextuality—was still missing. Here we provide such a component by introducing noncontextual wirings: a class of contextuality-free operations with a clear operational interpretation and a friendly parametrization. We characterize them completely for general black-box measurement devices with arbitrarily many inputs and outputs. As applications, we show that the relative entropy of contextuality is a contextuality monotone and that maximally contextual boxes that serve as contextuality bits exist for a broad class of scenarios. Our results complete a unified resource-theoretic framework for contextuality and Bell nonlocality.
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    Quantum theory allows for absolute maximal contextuality.
    (2015) Amaral, Barbara Lopes; Cunha, Marcelo de Oliveira Terra; Cabello Quintero, Adán
    Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality witnesses can be expressed as a sum S of n probabilities, and the independence number α and the Tsirelson-like number θ of the corresponding exclusivity graph are, respectively, the maximum of S for noncontextual theories and for the theory under consideration. A theory allows for absolute maximal contextuality if it has scenarios in which θ/α approaches n. Here we show that quantum theory allows for absolute maximal contextuality despite what is suggested by the examination of the quantum violations of Bell and noncontextuality inequalities considered in the past. Our proof is not constructive and does not single out explicit scenarios. Nevertheless, we identify scenarios in which quantum theory allows for almost-absolute-maximal contextuality.