We show that, under certain conditions, generalised contextuality, in the sense introduced by Spekkens, cannot be created from the vacuum of a quantum field. Initial noncontextual qudit states do not become contextual just by interacting with a quantum field. This is verified in two scenarios. First, in a perturbative approach where the time evolution operator is expanded in powers of the coupling constant. Second, in the limit of zero energy gap in the spectrum of the free detector Hamiltonian. Our results are at the opposite side of what has been recently obtained in the literature regarding the harvesting of Kochen-Specker contextuality. Our results demonstrate that the existing notions of contextuality can be independent of one another and that contextuality harvesting depends on which precise notion is used.
AI Summary
The paper asks whether coupling initially Spekkens-noncontextual families of finite-dimensional detector states to a scalar-field vacuum can generate generalised contextuality. It considers Unruh–DeWitt detectors comprising one qubit or $N$ qudits, with the field discarded after the interaction, and contrasts this question with previous contextuality-harvesting results using Kochen–Specker or sheaf-theoretic notions.
The central mathematical result is that an invertible quantum channel preserves noncontextuality of a preparation family when all POVMs are available, including for linearly dependent input families. The proof transports an existing ontological representation through the channel and its linear inverse. The detector–field channel is then shown to be invertible in two regimes. At any fixed perturbative order, it is a deformation of the identity and is invertible for sufficiently weak coupling. For gapless detectors, the Magnus expansion terminates exactly: in the joint eigenbasis of the detector coupling operators, the channel multiplies each matrix unit by a phase times a Gaussian factor, $\exp[-\operatorname{Var}(\Phi_{\boldsymbol l}-\Phi_{\boldsymbol k})/(2\hbar^2)]$. Finite smeared field variances make every multiplier nonzero, establishing the no-generation result for arbitrary finite $N$ and local dimension.
The exact calculation assumes gapless detectors, a free scalar-field vacuum or suitable Gaussian state, and finite smeared variances. Continuity also gives invertibility for sufficiently small gaps. No quantitative coupling or gap threshold is supplied. The general gapped channel is not calculated explicitly; extension to curved spacetime is proposed rather than demonstrated.
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Error found: Section 4 incorrectly concludes that the exact general-gapped detector channel is invertible because its perturbative approximants are invertible; invertible matrices can converge to a singular matrix.
The perturbative argument applies a preservation proposition requiring a genuine quantum channel without establishing complete positivity of the finite-order reduced map, although using the exact channel near zero coupling repairs this gap.
Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.
We show that, under certain conditions, generalised contextuality, in the sense introduced by Spekkens, cannot be created from the vacuum of a quantum field. Initial noncontextual qudit states do not become contextual just by interacting with a quantum field. This is verified in two scenarios. First, in a perturbative approach where the time evolution operator is expanded in powers of the coupling constant. Second, in the limit of zero energy gap in the spectrum of the free detector Hamiltonian. Our results are at the opposite side of what has been recently obtained in the literature regarding the harvesting of Kochen-Specker contextuality. Our results demonstrate that the existing notions of contextuality can be independent of one another and that contextuality harvesting depends on which precise notion is used.
The paper asks whether coupling initially Spekkens-noncontextual families of finite-dimensional detector states to a scalar-field vacuum can generate generalised contextuality. It considers Unruh–DeWitt detectors comprising one qubit or N qudits, with the field discarded after the interaction, and contrasts this question with previous contextuality-harvesting results using Kochen–Specker or sheaf-theoretic notions.
The central mathematical result is that an invertible quantum channel preserves noncontextuality of a preparation family when all POVMs are available, including for linearly dependent input families. The proof transports an existing ontological representation through the channel and its linear inverse. The detector–field channel is then shown to be invertible in two regimes. At any fixed perturbative order, it is a deformation of the identity and is invertible for sufficiently weak coupling. For gapless detectors, the Magnus expansion terminates exactly: in the joint eigenbasis of the detector coupling operators, the channel multiplies each matrix unit by a phase times a Gaussian factor, exp[−Var(Φl−Φk)/(2ℏ2)]. Finite smeared field variances make every multiplier nonzero, establishing the no-generation result for arbitrary finite N and local dimension.
The exact calculation assumes gapless detectors, a free scalar-field vacuum or suitable Gaussian state, and finite smeared variances. Continuity also gives invertibility for sufficiently small gaps. No quantitative coupling or gap threshold is supplied. The general gapped channel is not calculated explicitly; extension to curved spacetime is proposed rather than demonstrated.
In the literature, there are two differing definitions of contextuality: Kochen and Specker's, and Spekkens' (or ``generalised''). However, researchers using one of these definitions rarely consider the other, meaning comparative analysis of these two notions is rare. In this paper, we advance the idea that Kochen-Specker contextuality provides a generalisation of the idea of system being fundamentally \emph{nonclassical}, while Spekkens' noncontextuality provides a generalisation of the idea of a system being \emph{classical}. This allows us to reconcile the two approaches, as different stages in a hierarchy of classicality/nonclassicality.
Contextuality, a key resource for quantum advantage, describes systems in which the outcome of a measurement is not independent of other compatible measurements, in contrast to classical hidden-variable descriptions. We investigate the harvesting of contextuality from the vacuum of a quantum field using Unruh-DeWitt detectors. We show that localized interactions with the field can endow initially non-contextual detectors with contextuality with respect to Heisenberg-Weyl measurements, as quantified by contextual fraction. The harvested contextuality correlates with the emergence of Wigner function negativity, in agreement with known equivalences between these notions. Our results show that contextuality is a resource that can be extracted directly from the quantum vacuum and establish contextuality harvesting as a fundamental phenomenon in relativistic quantum information.
Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, understood as a resource for quantum computation, it is expected to hold the key to quantum advantage. Yet, despite its long recognised importance in quantum foundations and, more recently, in quantum computation, the structural essence of contextuality has remained somewhat elusive - different frameworks address different aspects of the phenomenon, yet their precise relationship often remains unclear. This issue already looms large at the level of the Bell-Kochen-Specker theorem: while traditional proofs proceed by showing the nonexistence of valuations, the notion of state-independent contextuality in the marginal approach allows to prove contextuality from seemingly weaker assumptions. In the light of this, and at the absence of a unified mathematical framework for Kochen-Specker contextuality, the original algebraic approach has been widely abandoned, in favour of the study of contextual correlations. Here, we reinstate the algebraic perspective on contextuality. Concretely, by building on the novel concept of context connections, we reformulate the algebraic relations between observables originally postulated by Kochen and Specker, and we explicitly demonstrate their consistency with the notion of state-independent contextuality. In the present paper, we focus on the new conceptual ideas and discuss them in the concrete setting of spin-1 observables, specifically those in the example of [S. Yu and C.H. Oh, Phys. Rev. Lett., 108, 030402 (2012)]; in a companion paper, we generalise these ideas, obtain a complete characterisation of Kochen-Specker contextuality and provide a detailed comparison with the related notions of contextuality in the marginal and graph-theoretic approach.
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements could not be viewed as deterministically revealing pre-existing properties of the system. More precisely, no model can assign deterministic outcomes to the projectors of a quantum measurement in a way that depends only on the projector and not the context (the full set of projectors) in which it appeared, despite the fact that the Born rule probabilities associated with projectors are independent of the context. A more general, operational definition of contextuality introduced by Spekkens, which we will term 'probabilistic contextuality', drops the assumption of determinism and allows for operations other than measurements to be considered contextual. Even two-dimensional quantum mechanics can be shown to be contextual under this generalised notion. Probabilistic noncontextuality represents the postulate that elements of an operational theory that cannot be distinguished from each other based on the statistics of arbitrarily many repeated experiments (they give rise to the same operational probabilities) are ontologically identical. In this paper, we introduce a framework that enables us to distinguish between different noncontextuality assumptions in terms of the relationships between the ontological representations of objects in the theory given a certain relation between their operational representations. This framework can be used to motivate and define a 'possibilistic' analogue, encapsulating the idea that elements of an operational theory that cannot be unambiguously distinguished operationally can also not be unambiguously distinguished ontologically. We then prove that possibilistic noncontextuality is equivalent to an alternative notion of noncontextuality proposed by Hardy. Finally, we demonstrate that these weaker noncontextuality assumptions are sufficient to prove alternative versions of known 'no-go' theorems that constrain ψ -epistemic models for quantum mechanics.
Quantum contextuality is the notion that certain measurement scenarios do not admit a global description of their statistics and has been implicated as the source of quantum advantage in a number of quantum information protocols. It has been shown that contextuality generalizes the concepts of nonlocal entanglement and magic and is an equivalent notion of nonclassicality to Wigner negativity. In this paper, the protocol of contextuality harvesting is introduced, and it is shown that Unruh-DeWitt models are capable of harvesting quantum contextuality from the vacuum of a massless scalar quantum field. In particular, it is shown that gapless systems can be made to harvest contextuality given a suitable choice of measurements. The harvested contextuality is also seen to behave similarly to harvested magic and can be larger in magnitude for specific parameter regimes. An Unruh-DeWitt qubit-qutrit system is also investigated, where it is shown that certain tradeoffs exist between the harvested contextuality of the qutrit and the harvested entanglement between the systems and that there are regimes where the two resources can both be present. Some of the tools of contextuality, namely the contextual fraction, are also imported and used as general measures for any form of harvested contextuality, including nonlocal entanglement and magic. Additionally, new criteria for genuine harvesting are put forward that also apply to individual systems, revealing new permissible harvesting parameter regimes.
In this thesis we explore the questions of what should be considered a "classical" theory, and which aspects of quantum theory cannot be captured by any theory that respects our intuition of classicality. This exploration is divided in two parts: in the first we review classical results of the literature, such as the Kochen-Specker theorem, von Neumann's theorem, Gleason's theorem, as well as more recent ideas, such as the distinction between ψ-ontic and ψ-epistemic ontological models, Spekkens' definition of contextuality, Hardy's ontological excess baggage theorem and the PBR theorem. The second part is concerned with pinning down what should be the "correct" definition of contextuality. We settle down on the definition advocated by Abramsky and Branderburger, motivated by the Fine theorem, and show the connection of this definition with the work of George Boole. This definition allows us to unify the notions of locality and noncontextuality, and use largely the same tools to characterize how quantum mechanics violates these notions of classicality. Exploring this formalism, we find a new family of noncontextuality inequalities. We conclude by reviewing the notion of state-independent contextuality.