Device-independent tests of classical and quantum dimensions

Abstract

We address the problem of testing the dimensionality of classical and quantum systems in a `black-box' scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension necessary to reproduce given measurement data. Furthermore, we generalise the concept of quantum dimension witnesses to arbitrary quantum systems, allowing one to place a lower bound on the Hilbert space dimension necessary to reproduce certain data. Illustrating these ideas, we provide simple examples of classical and quantum dimension witnesses.

To appear in PRL

References in corpus (6)

• Testing the Hilbert space dimension
• A lower bound on the dimension of a quantum system given measured data
• Unbounded violation of tripartite Bell inequalities
• Efficiency of higher dimensional Hilbert spaces for the violation of Bell inequalities
• Generalized Clauser-Horne-Shimony-Holt inequalities maximally violated by higher dimensional systems
• Economical ontological models for discrete quantum systems

Cited by in corpus (7)

• Semi-device-independent security of one-way quantum key distribution
• Dimension witnesses and quantum state discrimination
• Applying the simplest Kochen-Specker set for quantum information processing
• Bell inequalities for three systems and arbitrarily many measurement outcomes
• Nonlocality and Entanglement for Symmetric States
• Relation between semi- and fully-device-independent protocols
• Quantum discord in quantum random access codes and its connection with dimension witness