Robustness of Device Independent Dimension Witnesses

Abstract

Device independent dimension witnesses provide a lower bound on the dimensionality of classical and quantum systems in a "black box" scenario where only correlations between preparations, measurements and outcomes are considered. We address the problem of the robustness of dimension witnesses, namely that to witness the dimension of a system or to discriminate between its quantum or classical nature, even in the presence of loss. We consider the case when shared randomness is allowed between preparations and measurements and we provide a threshold in the detection efficiency such that dimension witnessing can still be performed.

8 pages, 5 figures, published version

References in corpus (6)

• Testing the Hilbert space dimension
• Device-independent tests of classical and quantum dimensions
• Semi-device-independent security of one-way quantum key distribution
• A lower bound on the dimension of a quantum system given measured data
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• Device-independent tests of quantum channels
• Properties of dimension witnesses and their semi-definite programming relaxations
• Device-independent tests of quantum measurements
• Relation between semi- and fully-device-independent protocols
• Shared randomness and device-independent dimension witnessing
• Compressibility of positive semidefinite factorizations and quantum models
• Accessible Information and Informational Power of Quantum 2-designs
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
• Certifying the Classical Simulation Cost of a Quantum Channel
• A general bound for the dimension of quantum behaviours in the prepare-and-measure scenario
• Interplays between classical and quantum entanglement-assisted communication scenarios
• Evidence-based certification of quantum dimensions
• Towards Necessary and sufficient state condition for violation of a multi-settings Bell inequality
• Device-independent tests of quantum states
• An unconditional experimental test of Nonclassicality
• Simultaneous Estimation of Dimension, States and Measurements: Computation of representative density matrices and POVMs
• Detection Efficiency Bounds in (Semi-)Device-Independent Scenarios
• Semi-device-independent randomness certification on discretized continuous-variable platforms
• Random Exclusion Codes: Quantum Advantages of Single-Shot Communication
• Quantum dimension test using the uncertainty principle
• Detection loophole attacks on semi-device-independent quantum and classical protocols