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A contextualidade da interferência condicional de dois fótons: um estudo em múltiplos cenários

Gilberto Ferreira Borges Júnior

Published Jun 7, 2013• 0 citations
OpenAlex

Abstract

In this work we test a family of noncontextuality inequalities developed from a unied view of several non-contextual scenarios, ie, a construction that allows unify seemingly disparate Gedankenexperiments used for quantum contextuality proofs, among which is the experiment that allows testing the CHSH inequality. Each of these inequalities predicts numerical limitations on the correlations of a physical system, when they are modeled by noncontextual theories. Violation of these inequalities shows that for a given scenario the correlations in the system can not be explained from a noncontextual viewpoint . The system which we want to test the contextual nature is two photonic qbits in the transversal path variable of twin photons generated by Spontaneous Parametric Down Conversion (SPDC). After being generated, the photon pairs cross a double-slit and exit it in a entangled state in path variables. Violation of the non-contextual inequalities for different measurement scenariosdemonstrates that the nonlocal conditionality displayed in the Youngexperiment with photons generated by SPDC, can not be properly explained by a local deterministic model, i.e, can not be explained in scope of a non-contextual hidden variable theory.

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In this work we test a family of noncontextuality inequalities developed from a unied view of several non-contextual scenarios, ie, a construction that allows unify seemingly disparate Gedankenexperiments used for quantum contextuality proofs, among which is the experiment that allows testing the CHSH inequality. Each of these inequalities predicts numerical limitations on the correlations of a physical system, when they are modeled by noncontextual theories. Violation of these inequalities shows that for a given scenario the correlations in the system can not be explained from a noncontextual viewpoint . The system which we want to test the contextual nature is two photonic qbits in the transversal path variable of twin photons generated by Spontaneous Parametric Down Conversion (SPDC). After being generated, the photon pairs cross a double-slit and exit it in a entangled state in path variables. Violation of the non-contextual inequalities for different measurement scenariosdemonstrates that the nonlocal conditionality displayed in the Youngexperiment with photons generated by SPDC, can not be properly explained by a local deterministic model, i.e, can not be explained in scope of a non-contextual hidden variable theory.
The violation of contextuality inequalities shows a strong conflict between the noncontextual hidden variable theory and quantum mechanics. A single qutrit is the simplest indivisible quantum system that can allow a state-dependent contextuality test with five observables and a state-independent contextuality test with 13 observables. For any qutrit states, except for the maximally mixed state, one can always find a set of nine observables for which the corresponding inequality is violated [P. Kurzynski and D. Kaszlikowski, Phys. Rev. A 86, 042125 (2012)]. In this paper, we demonstrate the violation of this inequality using single-photon experiments. Our experiments not only enrich the tests of quantum contextuality, but also deepen the understanding of the physical nature of quantum mechanics.
We show that correlations between the detector positions at the two-photon Young interference plane exhibit contextual behavior. Contextuality is demonstrated by showing the violation of the nnn-cycle noncontextuality inequalities [M. Ara\'ujo et al., Phys. Rev. A 88, 022118 (2013)] for any even number nnn of observables ranging from 4 to 14. These violations exclude noncontextual hidden-variable theories as an explanation of the conditional two-photon Young pattern. Unlike recent contextuality experiments, ours is free of the compatibility loophole.
Bell nonlocality and quantum contextuality are two important resources which, however, behave very differently in many tasks where the quantum correlation has an edge over its classical counterpart. In this work, we directly compare these two behaviors, which via the Cabello-Severini-Winter graph-theoretical approach, can be associated with a same exclusivity graph. In particular, we consider the exclusivity graph that leads to I3322{I}_{3322}I3322​-type inequalities in the Bell and the contextual scenarios, respectively. We find that maximal violation of Bell inequality is around 6.251, and maximal violation of the noncontextuality inequality is around 6.588 for a five-dimensional system and 6.571 for a four-dimensional system, respectively. The results predict a gap of $\mathrm{\ensuremath{\Delta}}\ensuremath{\approx}0.32$ between quantum contextuality and Bell nonlocality. We then present an experimental observation of the gap by employing both the maximally entangled photon pairs from the spontaneous parametric down-conversion process and the single photons encoded into qudits from an intrinsic defect in gallium nitride. Our results will further deepen the understanding of different types of quantum correlations.
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.
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.
Quantum contextuality provides a fundamental signature of nonclassical behavior that cannot be explained by noncontextual hidden-variable models. We propose and experimentally implement a linear-optical setup for demonstrating Kochen-Specker contextuality via a violation of the KCBS inequality using single photons. Our scheme employs sequential measurements realized with linear-optical networks and on-off photodetectors. The construction ensures that each co-measured observable is implemented by the same physical operation across different contexts. Our experimental results demonstrate a clear violation of the KCBS inequality and robustness against photon loss. Beyond fundamental investigations, the proposed setup provides a practical tool for probing non-classicality and photon-number statistics of quantum states, which in turn enables the verification of single-photon sources.