Characterising and bounding the set of quantum behaviours in contextuality scenarios

Abstract

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.

arXiv commentRevised version, accepted in Quantum

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• Semidefinite programming relaxations for quantum correlations
• Aspects of the phenomenology of interference that are genuinely nonclassical
• Noise-robust preparation contextuality shared between any number of observers via unsharp measurements
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• Semi-definite programming and quantum information
• Coherence and contextuality in a Mach-Zehnder interferometer
• An invertible map between Bell non-local and contextuality scenarios
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Mutually Unbiased Balanced Functions & Generalized Random Access Codes
• Bounding and simulating contextual correlations in quantum theory
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• Failure of epistemic models to explain the antidistinguishability of quantum mixed preparations
• Partial ignorance communication tasks in quantum theory
• Quantum description of reality is epistemically incomplete
• Limits of Classical correlations and Quantum advantages under (Anti-)Distinguishability constraints in Multipartite Communication