Informationally restricted correlations: a general framework for classical and quantum systems

Abstract

We introduce new methods and tools to study and characterise classical and quantum correlations emerging from prepare-and-measure experiments with informationally restricted communication. We consider the most general kind of informationally restricted correlations, namely the ones formed when the sender is allowed to prepare statistical mixtures of mixed states, showing that contrary to what happens in Bell nonlocality, mixed states can outperform pure ones. We then leverage these tools to derive device-independent witnesses of the information content of quantum communication, witnesses for different quantum information resources, and demonstrate that these methods can be used to develop a new avenue for semi-device independent random number generators.

References in corpus (10)

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• Testing the Hilbert space dimension
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• Semi-device-independent security of one-way quantum key distribution
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Cited by in corpus (23)

• Bell nonlocality in networks
• Semidefinite programming relaxations for quantum correlations
• Entanglement-assisted quantum communication with simple measurements
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Entanglement detection with imprecise measurements
• Entanglement in prepare-and-measure scenarios: many questions, a few answers
• Semi-definite programming and quantum information
• Almost qudits in the prepare-and-measure scenario
• Bounding and simulating contextual correlations in quantum theory
• Unbounded quantum advantage in communication complexity measured by distinguishability
• Prepare-and-measure scenarios with photon-number constraints
• Interplays between classical and quantum entanglement-assisted communication scenarios
• Information capacity of quantum communication under natural physical assumptions
• Connecting XOR and XOR* games
• Certifying nonstabilizerness in quantum processors
• Theory-independent randomness generation from spatial symmetries
• Absolute dimensionality of quantum ensembles
• A coherence-witnessing game and applications to semi-device-independent quantum key distribution
• Partial ignorance communication tasks in quantum theory
• Semi-device-independent randomness certification on discretized continuous-variable platforms
• Quantum description of reality is epistemically incomplete
• Quantum inputs in the prepare-and-measure scenario and stochastic teleportation
• Limits of Classical correlations and Quantum advantages under (Anti-)Distinguishability constraints in Multipartite Communication