Contextuality in entanglement-assisted one-shot classical communication

Abstract

We consider the problem of entanglement-assisted one-shot classical communication. In the zero-error regime, entanglement can increase the one-shot zero-error capacity of a family of classical channels following the strategy of Cubitt et al., Phys. Rev. Lett. 104, 230503 (2010). This strategy uses the Kochen-Specker theorem which is applicable only to projective measurements. As such, in the regime of noisy states and/or measurements, this strategy cannot increase the capacity. To accommodate generically noisy situations, we examine the one-shot success probability of sending a fixed number of classical messages. We show that preparation contextuality powers the quantum advantage in this task, increasing the one-shot success probability beyond its classical maximum. Our treatment extends beyond Cubitt et al. and includes, for example, the experimentally implemented protocol of Prevedel et al., Phys. Rev. Lett. 106, 110505 (2011). We then show a mapping between this communication task and a corresponding nonlocal game. This mapping generalizes the connection with pseudotelepathy games previously noted in the zero-error case. Finally, after motivating a constraint we term context-independent guessing, we show that contextuality witnessed by noise-robust noncontextuality inequalities obtained in R. Kunjwal, Quantum 4, 219 (2020), is sufficient for enhancing the one-shot success probability. This provides an operational meaning to these inequalities and the associated hypergraph invariant, the weighted max-predictability, introduced in R. Kunjwal, Quantum 3, 184 (2019). Our results show that the task of entanglement-assisted one-shot classical communication provides a fertile ground to study the interplay of the Kochen-Specker theorem, Spekkens contextuality, and Bell nonlocality.

arXiv comment25 pages, 4 figures, Accepted in Quantum

References in corpus (40)

• Bell nonlocality
• Hidden Variables and the Two Theorems of John Bell
• Contextuality for preparations, transformations, and unsharp measurements
• Contextuality supplies the magic for quantum computation
• A simple test for hidden variables in spin-1 system
• Bell-Kochen-Specker theorem: A proof with 18 vectors
• An experimental test of noncontextuality without unwarranted idealizations
• Preparation contextuality powers parity-oblivious multiplexing
• A Combinatorial Approach to Nonlocality and Contextuality
• Quantum Pseudo-Telepathy
• Improving zero-error classical communication with entanglement
• Contextual advantage for state discrimination
• Maximally epistemic interpretations of the quantum state and contextuality
• Anomalous weak values and contextuality: robustness, tightness, and imaginary parts
• From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism
• Optimal bounds for parity-oblivious random access codes
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Zero-error channel capacity and simulation assisted by non-local correlations
• State independent contextuality advances one-way communication
• Measurement incompatibility and steering are necessary and sufficient for operational contextuality
• Quantum realization of arbitrary joint measurability structures
• Experimentally bounding deviations from quantum theory in the landscape of generalized probabilistic theories
• Contextual advantage for state-dependent cloning
• Preparation contextuality as an essential feature underlying quantum communication advantage
• Robust preparation noncontextuality inequalities in the simplest scenario
• What does an experimental test of quantum contextuality prove or disprove?
• Entanglement-Enhanced Classical Communication over a Noisy Classical Channel
• From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities
• Measurement sharpness cuts nonlocality and contextuality in every physical theory
• Experimental generalized contextuality with single-photon qubits
• Minimal state-dependent proof of measurement contextuality for a qubit
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Ontological models, preparation contextuality and nonlocality
• Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem
• The ontological identity of empirical indiscernibles: Leibniz's methodological principle and its significance in the work of Einstein
• Contextuality beyond the Kochen-Specker theorem
• Joint measurability structures realizable with qubit measurements: incompatibility via marginal surgery
• Inaccessible information in probabilistic models of quantum systems, non-contextuality inequalities and noise thresholds for contextuality
• Contextuality without access to a tomographically complete set
• On optimal entanglement assisted one-shot classical communication

Cited by in corpus (16)

• Why interference phenomena do not capture the essence of quantum theory
• Aspects of the phenomenology of interference that are genuinely nonclassical
• Characterising and bounding the set of quantum behaviours in contextuality scenarios
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Contextuality without incompatibility
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• A mathematical framework for operational fine tunings
• A linear program for testing nonclassicality and an open-source implementation
• Contextuality with vanishing coherence and maximal robustness to dephasing
• Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
• Alternative robust ways of witnessing nonclassicality in the simplest scenario
• Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
• Connecting XOR and XOR* games
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory
• Typicality of Contextuality