The study of ontology (hidden variables) provides for a vital ground on which significant nonclassical features of quantum theory are revealed. One such nonclassical ontic feature is preparation contextuality (PC) and advantage in oblivious communication tasks is one of its operational signatures. This article primarily pursues the ontic feature underlying quantum advantage in communication complexity (CC). We construct oblivious communication tasks tailored to given CC problems. We upper bound the classical success probability of these oblivious communication tasks, obtaining preparation noncontextual inequalities. We use the very states and measurements responsible for advantage in CC problems along with the orthogonal mixtures of these states to orchestrate an advantageous protocol for the associated oblivious communication tasks and the violation of the associated inequalities, thereby unveiling PC. To showcase the vitality of our results, we find a criterion for unbounded violation of these inequalities and demonstrate the same for two widely studied CC problems.
The study of ontology (hidden variables) provides for a vital ground on which significant nonclassical features of quantum theory are revealed. One such nonclassical ontic feature is preparation contextuality (PC) and advantage in oblivious communication tasks is one of its operational signatures. This article primarily pursues the ontic feature underlying quantum advantage in communication complexity (CC). We construct oblivious communication tasks tailored to given CC problems. We upper bound the classical success probability of these oblivious communication tasks, obtaining preparation noncontextual inequalities. We use the very states and measurements responsible for advantage in CC problems along with the orthogonal mixtures of these states to orchestrate an advantageous protocol for the associated oblivious communication tasks and the violation of the associated inequalities, thereby unveiling PC. To showcase the vitality of our results, we find a criterion for unbounded violation of these inequalities and demonstrate the same for two widely studied CC problems.
Abstract Although ‘quantum contextuality’ is one of the most fundamental non-classical feature, its generic role in information processing and computation is an open quest. In this article, we present a family of distributed computing tasks pertaining to every logical proof of Kochen–Specker (KS) contextuality in two different one-way communication scenarios: (I) communication of bounded dimensional system, (II) communication of unbounded dimensional system while keeping certain information oblivious, namely, oblivious communication (OC). As the later remains largely unexplored, we introduce a general framework for OC tasks and provide a methodology for obtaining an upper bound on the success of OC tasks in classical communication. We show that quantum communication comprised of every KS set of vectors outperforms classical communication and perfectly accomplish the task in both the aforementioned scenarios. We explicitly discuss the communication tasks pertaining to the simplest state independent contextuality sets of dimension three and four. Our results establish an operational significance to single system contextuality and open up the possibility of semi-device independent quantum information processing based on that. Alongside, we identify any advantage in OC tasks as a witness of preparation contextuality.
The quantum ontological feature of contextuality apart from being central to foundations of quantum theory forms the basis of quantum advantage in a multitude of information processing tasks. In particular, the contextuality of preparation procedures was shown to power a particular two-party information processing task “parity oblivious multiplexing” (Spekkens et al. Phys Rev Lett 102:010401 (2009). Specifically, it was shown that there exists a limit to how well any preparation noncontextual theory can perform in this task. This limit constitutes a noncontextuality inequality. Moreover, the authors demonstrated quantum violation of this inequality along with preparation contextuality associated with the ontic description underlying two-level completely mixed quantum state. In this work, we extend these arguments to apply to arbitrary dimensions by introducing a class of two-party information processing tasks, namely d-level parity oblivious random access codes. We analytically obtain classical (or equivalently preparation noncontextual) bounds on the success probability for these tasks for arbitrary d. For each value of d, this bound constitutes a unique noncontextuality inequality. Remarkably, these bounds are independent of the amount of communication. Furthermore, we find a classical protocol utilizing a dc=d -dimensional classical message which saturates this bound. In order to establish nontriviality of these inequalities, we provide evidence of significant quantum violations. Specifically, by numerical techniques, we show that for d=3,…,10 , the noncontextuality bound is violated by quantum theory. (1) We provide explicit quantum protocols which violate the associated noncontextuality inequality for d=3,4,5 employing dq=d -leveled quantum systems. (2) Using see-saw semi-definite programming (SDP) technique, we find evidence (lower bounds) of significant quantum violation of these inequalities for d=3,…,10 . (3) With the help of state-of-the-art (NPA-hierarchy like) SDP technique, we provide upper bounds (independent of the dimension of the involved quantum systems) on quantum violation for d=3,…,10 . The introduced class of information tasks, thus, provides for operational depiction of preparation contextuality of the ontic description underlying mixed higher dimensional quantum systems.
The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations, we demonstrate monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.
Preparation contextuality is often manifested operationally through a quantitative advantage over preparation-noncontextual models in information-processing tasks, yet quantum theory typically falls short of perfect success. Here we introduce a parity-oblivious Hidden Matching task that instead yields an all-vs-nothing manifestation of preparation contextuality. Alice encodes an n-bit string so that her message reveals no information about any input parity other than the two-bit parities. Bob, given a perfect matching on the input positions, must output an edge of the matching together with the parity of its two bits. A quantum protocol using a single ⌈log2n⌉-qubit message satisfies the parity-obliviousness constraint and succeeds with certainty. We prove that no preparation-noncontextual model achieves perfect success for any even n≥6. The result holds for arbitrary ontic state spaces and assumes neither outcome determinism nor measurement noncontextuality. For n=6 and n=8, the optimal noncontextual success probabilities are 4/5 and 3/4, respectively, while asymptotically the optimal noncontextual success probability is 1/2+Θ(1/n). Our asymptotic upper bound follows from a Fourier-analytic sum rule derived via hypercontractivity on the Boolean hypercube. The resulting separation is qualitative rather than merely quantitative: quantum theory achieves perfect success, whereas preparation-noncontextual models cannot. We aslo show that at n=8 the noncontextual bound remains 3/4 even when Bob is restricted to just suitable 4 of the 105 possible perfect matchings, bringing the effect within experimental reach.
An ontological model of an operational theory is considered to be universally noncontextual if both preparation and measurement noncontextuality assumptions are satisfied in that model. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely linked to suitable Bell expression whose local bound is greater than universal non-contextual bound. Thus, for a given state, even if quantum theory does not exhibit non-locality, it may still reveal non-classicality by violating the universal non-contextual bound. Further, we consider a different communication game to demonstrate that for a given choices of observables in quantum theory, even if there is no logical proof of preparation and measurement contextuality exist, the universal quantum contextuality can be revealed through that communication game. Such a game thus test a weaker form of universal non-contextuality with minimal assumption.
Replacing the task of retrieval with exclusion changes how preparation contextuality manifests operationally under parity-oblivious constraints, with exclusion showing a quantum advantage where retrieval does not. We introduce the parity-oblivious random exclusion code (POREC) and show that for prime symbol size m, classical and preparation-noncontextual encodings provide a tight noncontextual bound. For the first nontrivial case (two digits, three symbols), our derived exact qubit optimum violates this bound, in contrast to parity-oblivious retrieval, which displays no quantum advantage. This characteristic difference is absent without parity constraints. For general prime m, qubit strategies achieve a quantum-to-noncontextual gap that grows linearly relative to the random exclusion code (REC) gap, exceeding both parity-oblivious retrieval and standard REC. The exact qubit bound yields a sharp semi-device-independent certification of dimension d≥3. Our analysis of noise robustness demonstrates POREC to be amenable for experimental implementation on existing prepare-and-measure platforms, establishing parity-oblivious exclusion as a distinct operational probe of preparation contextuality, as well as a practical information processing protocol with wide applications.