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Are we witnessing non-classical phenomena when noncontextuality inequalities are violated?.

Alisson Tezzin

Published Nov 1, 2021• 0 citations
OpenAlex

Abstract

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.

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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.
Recent research on quantum contextuality has been strongly centered on device-independent frameworks, such as the many graph approaches to contextuality and the celebrated sheaf-theoretical approach. Contextuality is described in these frameworks as a property of data only, making it possible to characterize and quantify the phenomena regardless of the reasons why it occurs. In this paper we look beyond the data and focus on possible explanations for this experimental fact. We show that a classical system generating contextual data can easily be found if the following conditions are satisfied (1) We only have access to a specific collection of epistemic measurements (which, all things considered, is basically Bohr's view on quantum measurements) and (2) There is a limitation on which of these measurements can be jointly performed. The way we see it, this example indicates that contextuality may be a consequence of the type of measurement taken into account, instead of an intrinsic feature of the system upon which these measurements are performed; if this is correct, the widespread idea that quantum contextuality is a non-classical feature can be avoided.
Contextuality is a fundamental manifestation of nonclassicality, indicating that for certain quantum correlations, sets of jointly measurable variables cannot be pre-assigned values independently of the measurement context. In this work, we characterize nonclassical quantum correlation beyond contextuality, in terms of supernoncontextuality, namely the higher-than-quantum hidden-variable (HV) dimensionality required to reproduce the given noncontextual quantum correlations. Thus supernoncontextuality is the contextuality analogue of superlocality. Specifically, we study the quantum system of two-qubit states in a scenario composed of five contexts that demonstrate contextuality in a state-dependent fashion. For this purpose, we use the framework of boxes, whose behavior is described by a set of probabilities satisfying the no-disturbance conditions. We first demonstrate that while superlocality is necessary to observe a contextual box, superlocality is not sufficient for contextuality. On the other hand, a noncontextual superlocal box can be supernoncontextual, but superlocality is not a necessary condition. We then introduce a notion of nonclassicality beyond the standard contextuality, called semi-device-independent contextuality. We study semi-device-independent contextuality of two-qubit states in the above-mentioned scenario and demonstrate how supernoncontextuality implies this nonclassicality. To this end, we propose a criterion and a measure of semi-device-independent contextuality.
Contextuality is one way of capturing the nonclassicality of quantum theory.The contextual nature of a theory is often witnessed via the violation of noncontextuality inequalities-certain linear inequalities involving probabilities of measurement events.Using the exclusivity graph approach (one of the two main graph theoretic approaches for studying contextuality), it was shown [Cabello et al.Phys. Rev. A 88, 032104 (2013); Chudnovsky et al.Ann. Math. 164, 51 (2006)] that a necessary and sufficient condition for witnessing contextuality is the presence of an odd number of events (greater than three) which are either cyclically or anticyclically exclusive.Thus, the noncontextuality inequalities the underlying exclusivity structure of which is as stated, either cyclic or anticyclic, are fundamental to quantum theory.We show that there is a unique noncontextuality inequality for each nontrivial cycle and anticycle.In addition to the foundational interest, we expect this to aid the understanding of contextuality as a resource to quantum computing and its applications to local self-testing.
This PhD-thesis is based on the five experiments I have performed during mytime as a PhD-student. Three experiments are implementations of non-contextualinequalities and two are implementations of witness functions for classical- andquantum dimensions of sets of states. A dimension witness is an operator function that produce a value whenapplied to a set of states. This value has different upper bounds depending onthe dimension of the set of states and also depending on if the states are classicalor quantum. Therefore a dimension witness can only give a lower bound on thedimension of the set of states.The first dimension witness is based on the CHSH-inequality and has theability of discriminating between classical and quantum sets of states of two andthree dimensions, it can also indicate if a set of states must be of dimension fouror higher.The second dimension witness is based on a set theoretical representationof the possible combinations of states and measurements and grows with thedimension of the set of states you want to be able to identify, on the other handthere is a formula for expanding it to arbitrary dimension.Non-contextual hidden variable models is a family of hidden variable modelswhich include local hidden variable models, so in a sence non-contextual inequal-ities are a generalisation of Bell-inequalities. The experiments presented in this thesis all use single particle quantum systems.The first experiment is a violation of the KCBS-inequality, this is the simplest correlation inequality which is violated by quantum mechanics.The second experiment is a violation of the Wright-inequality which is the simplest inequality violated by quantum mechanics, it contains only projectors and not correlations.The final experiment of the thesis is an implementation of a Hardy-like equality for non-contextuality, this means that the operators in the KCBS-inequality have been rotated so that one term in the sum will be zero for all non-contextual hidden variable models and we get a contradiction since quantum mechanicsgives a non-zero value for all terms.
Contextuality is thought of as an intrinsic signature of non-classicality, and a crucial resource for achieving unique advantages of quantum information processing. However, recently there have been debates on whether classical fields may also demonstrate contextuality. Here we experimentally test a fundamental non-contextual (NC) inequality with both quantum and classical optical systems. In particular, we apply identical measurements on both systems, therefore provide a unified comparison between them. The results show that although the quantum system provides a clear violation of the NC inequality, the violations with the classical system strongly depend on the specific definition of the measurement event which is equivalent to filtering the non-classical component of the input state. Our results link the contextual correlations to non-classical quasi-distributions of optical states, and elucidate the resources required for classical systems to achieve the quantum bound.
Contextuality is regarded as a nonclassical feature, challenging our everyday intuition; quantum contextuality is currently seen as a resource for many applications in quantum computation, being responsible for quantum advantage over classical analogs. In our work, we adapt the NNN-cycle scenarios with odd NNN to multiple independent observers which measure the system sequentially. We analyze the possibility of violating the inequalities as a function of the number of observers and under different measurement protocols. We then reinterpret the results as an open quantum system where the environment is divided into fragments. In this context, the results show the emergence of noncontextuality in such a setting, bringing together the quantum behavior to our classical experience. We then compare such emergence of noncontextuality with that of objectivity under the ``environment as a witness'' paradigm.