Dimension witnesses and quantum state discrimination

Abstract

Dimension witnesses allow one to test the dimension of an unknown physical system in a device-independent manner, that is, without placing assumptions about the functioning of the devices used in the experiment. Here we present simple and general dimension witnesses for quantum systems of arbitrary Hilbert space dimension. Our approach is deeply connected to the problem of quantum state discrimination, hence establishing a strong link between these two research topics. Finally, our dimension witnesses can distinguish between classical and quantum systems of the same dimension, making them potentially useful for quantum information processing.

5 pages

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
• Unbounded violation of tripartite Bell inequalities
• Efficiency of higher dimensional Hilbert spaces for the violation of Bell inequalities

Cited by in corpus (16)

• Quantum state discrimination and its applications
• Bounding the set of finite dimensional quantum correlations
• Operational relevance of resource theories of quantum measurements
• Device-independent certification of high-dimensional quantum systems
• Bound on Ergotropic Gap for Bipartite Separable States
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• Device-independent certification of Hilbert space dimension using a family of Bell expressions
• Semi-device-independent certification of entanglement in superdense coding
• Shared randomness and device-independent dimension witnessing
• Device-independent self-testing of unsharp measurements
• Sharing preparation contextuality in Bell experiment by arbitrary pair of sequential observers
• Entanglement Verification of Hyperentangled Photon Pairs
• Optimal classical and quantum real and complex dimension witness
• Dimensionality Distinguishers
• Quantum Random Access Codes Implementation for Resource Allocation and Coexistence with Classical Telecommunication
• Quantum dimension test using the uncertainty principle