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arXiv:1811.00615 · Physical Review A

Classical limits and contextuality in a scenario of multiple observers

Roberto D. Baldijão, Marcelo Terra Cunha

Published Nov 30, 2020• 5 citations
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Abstract

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 $N$-cycle scenarios with odd $N$ 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.

DOI
10.1103/physreva.102.052226

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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.
Contextuality is a fundamental marker of quantum non-classicality, which has emerged as a key resource for quantum computational advantage in multiple settings. Many such results hinge specifically on contextuality witnessed through Pauli measurements. In this work, we initiate a systematic study of (state-dependent) Pauli contextuality, focusing on cycle measurement scenarios, the simplest scenarios capable of exhibiting contextual behaviour. First, we study realizability of cycle scenarios with multi-qubit Pauli observables: we show that the maximum size of a cycle faithfully realizable by mmm-qubit Paulis is upper bounded by 3m3m3m, while we construct explicit realizations of cycles of size 2m−12m-12m−1 or 2m2m2m, depending on whether m≢1(mod3)m \not\equiv 1 \pmod{3}m≡1(mod3) or m≡1(mod3)m \equiv 1 \pmod{3}m≡1(mod3). Then, we investigate the presence of contextuality: we prove that no nnn-cycle Pauli realization for n>4n > 4n>4 can witness contextuality (on any quantum state), whereas for n=4n = 4n=4 every Pauli realization exhibits contextuality, attaining the quantum bound for all noncontextuality inequalities on some pure state. Finally, we discuss arbitrary Pauli scenarios in light of Vorob'ev's theorem, and show that, contrary to what our cycle characterization might suggest, the presence of 444-cycles is not necessary for witnessing contextuality in general Pauli scenarios.
KS-contextuality is a crucial feature of quantum theory. Previous research demonstrated the vanishing of NNN-cycle KS-contextuality in setups where multiple independent observers measure sequentially on the same system, which we call Public Systems. This phenomenon can be explained as the additional observers' measurements degrading the state and depleting the quantum resource. This explanation would imply that state-independent contextuality should survive in such a system. In this paper, we show that this is not the case. We achieved this result by simulating an observer trying to violate the Peres-Mermin noncontextuality inequality in a Public System. Additionally, we provide an analytical description of our setup, explaining the loss of contextuality even in the state-independent case. Ultimately, these results show that state-independent contextuality is not independent of what happens to the system in-between the measurements of a context.
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 emergence of classicality is fundamentally driven by the interaction between a quantum system and its environment. Foundational open-system approaches, notably the Caldeira-Leggett model, successfully captured how these interactions lead to macroscopic effects like quantum dissipation and decoherence. However, these approaches often leave the precise definitions of classicality and quantumness ambiguous. In quantum information theory, this boundary is a heavily scrutinized question, and Kochen-Specker contextuality emerges as a hallmark of nonclassicality. It is therefore natural to investigate whether decoherence can actually suppress this property. Taking this path creates an apparent conundrum, once there exist two distinct manifestations of quantum contextuality: state-dependent and state-independent ones. While state-dependent contextuality naturally vanishes under state degradation, state-independent contextuality could persist for any quantum state, since it shows up even for the maximally mixed state! In this paper, we resolve this apparent paradox by analyzing sequential measurement implementations of the paradigmatic Klyachko, Can, Binicioğlu, and Shumovsky (KCBS) and Peres-Mermin prepare-and-measure scenarios under the influence of depolarizing channels. By introducing noise both prior to and in between measurements, and by analyzing the resulting sequential correlators in both the Schrödinger and Heisenberg pictures, we show how open-system dynamics suppress the correlations required to witness contextuality, leading to classicalization.
In this paper we analyze the notion of measurement noncontextuality (MNC) and identify contextual scenarios which involve sequential measurements of only a single measurement device. We show that any noncontextual ontological model fails to explain the statistics of outcomes of a single carefully constructed positive-operator-valued measure (POVM) executed sequentially on a quantum system. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the noncontextual (NC) ontic model, and construct a quantum situation involving measurements from the Klyachko-Can-Binicio\ifmmode \check{g}\else \v{g}\fi{}lu-Shumovsky (KCBS) inequality. We show that the resultant statistics arising from this device violate our NC inequality. This device can be generalized by incorporating measurements from arbitrary nnn-cycle contextuality inequalities of which n=5n=5n=5 corresponds to the KCBS inequality. We show that the NC and quantum bounds for various scenarios can be derived more easily using only the functional relationships between the outcomes for larger values nnn. This makes it one of the simpler contextual inequalities to analyze.
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.