Device-Independent Tests of Entropy

Abstract

We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on the communication entropy, given observable data. The first method is based on the framework of causal inference networks. The second technique, based on convex optimization, shows that quantum communication provides an advantage over classical, in the sense of requiring a lower entropy to reproduce given data. These ideas may serve as a basis for novel applications in device-independent quantum information processing.

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Cited by in corpus (43)

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• Towards device-independent information processing on general quantum networks
• Causal modeling the delayed choice experiment
• Entropic nonsignaling correlations
• Informationally restricted quantum correlations
• Informationally restricted correlations: a general framework for classical and quantum systems
• Bell scenarios with communication
• Device-independent tests of quantum channels
• Covariance Bell inequalities
• Device independent certification of a quantum delayed choice experiment
• Semi-device-independent certification of entanglement in superdense coding
• A universal scheme for robust self-testing in the prepare-and-measure scenario
• Device-independent tests of quantum measurements
• The entropic approach to causal correlations
• Semidefinite tests for latent causal structures
• Almost qudits in the prepare-and-measure scenario
• Indistinguishability of causal relations from limited marginals
• Probing the Non-Classicality of Temporal Correlations
• Device-independent dimension tests in the prepare-and-measure scenario
• Simple Information Processing Tasks with Unbounded Quantum Advantage
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Semi-device-independent characterization of quantum measurements under a minimum overlap assumption
• Quantum steering beyond instrumental causal networks
• Certifying the purity of quantum states with temporal correlations
• Information complementarity in multipartite quantum states and security in cryptography
• Monogamy of Temporal Correlations: Witnessing non-Markovianity Beyond Data Processing
• Experimental device-independent tests of quantum channels
• Computational tools for solving a marginal problem with applications in Bell non-locality and causal modeling
• Device-independent certification of non-classical joint measurements via causal models
• Device-independent characterizations of a shared quantum state independent of any Bell inequalities
• Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
• Prepare-and-Magic: Semi-Device Independent Magic Certification in the Prepare-and-Measure Scenario
• Modified quantum delayed-choice experiment without quantum control
• Maximal Elements of Quantum Communication
• Characterizing nonbilocal correlation: A geometric perspective
• Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
• Experimental Device-Independent Tests of Classical and Quantum Entropy
• Semi-device-independent randomness certification on discretized continuous-variable platforms
• Experimental certification of ensembles of high-dimensional quantum states with independent quantum devices
• Characterizing nonclassical correlations of tensorizing states in a bilocal scenario
• Quantifying measurement-induced nonbilocal correlation