Certifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses

• Published in: Physical review letters Vol. 120; no. 23; p. 230503
• Main Authors: Aguilar, Edgar A, Farkas, Máté, Martínez, Daniel, Alvarado, Matías, Cariñe, Jaime, Xavier, Guilherme B, Barra, Johanna F, Cañas, Gustavo, Pawłowski, Marcin, Lima, Gustavo
• Format: Journal Article
• Language: English
• Published: United States American Physical Society 08-06-2018
• Subjects: Coding; Decomposition; Photonics; Quantum phenomena; Quantum theory; Random access
• ISSN: 0031-9007; 1079-7114; 1079-7114
• DOI: 10.1103/PhysRevLett.120.230503

We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique, we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using noncoupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.