Testing dimension and non-classicality in communication networks

Abstract

We consider networks featuring preparation, transformation, and measurement devices, in which devices exchange communication via mediating physical systems. We investigate the problem of testing the dimension of the mediating systems in the device-independent scenario, that is, based on observable data alone. A general framework for tackling this problem is presented, considering both classical and quantum systems. These methods can then also be used to certify the non-classicality of the mediating systems, given an upper bound on their dimension. Several case studies are reported, which illustrate the relevance of the framework. These examples also show that, for fixed dimension, quantum systems largely outperform classical ones. Moreover, the use of a transformation device considerably improves noise tolerance when compared to simple prepare-and-measure networks. These results suggest that the classical simulation of quantum systems becomes costly in terms of dimension, even for simple networks.

11 pages, published version

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• Testing the Hilbert space dimension
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• Unbounded violation of tripartite Bell inequalities
• Dimension witnesses and quantum state discrimination
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• Device-independent certification of entangled measurements
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• Dimension of physical systems, information processing, and thermodynamics
• Experimental semi-device-independent certification of entangled measurements

Cited by in corpus (25)

• Self-testing quantum states and measurements in the prepare-and-measure scenario
• Self-testing entangled measurements in quantum networks
• Leggett-Garg macrorealism and the quantum nondisturbance conditions
• Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
• Device-independent certification of Hilbert space dimension using a family of Bell expressions
• Leggett-Garg Macrorealism and temporal correlations
• Semi-device-independent certification of entanglement in superdense coding
• Memory cost of temporal correlations
• Complementarity between entanglement-assisted and quantum distributed random access code
• Genuine temporal correlations can certify the quantum dimension
• Temporal correlations in the simplest measurement sequences
• Probing the Non-Classicality of Temporal Correlations
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Ticking-clock performance enhanced by nonclassical temporal correlations
• Simulating extremal temporal correlations
• Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
• Structure of dimension-bounded temporal correlations
• Interplays between classical and quantum entanglement-assisted communication scenarios
• Device-independent certification of non-classical joint measurements via causal models
• Multiparty quantum random access codes
• Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages
• Classical bounds on two-outcome bipartite Bell expressions and linear prepare-and-measure witnesses: Efficient computation in parallel environments such as graphics processing units
• Certifying asymmetry in the configuration of three qubits
• Limits of Classical correlations and Quantum advantages under (Anti-)Distinguishability constraints in Multipartite Communication
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements