Witnessing irreducible dimension
Wan Cong, Yu Cai, Jean-Daniel Bancal, Valerio Scarani

TL;DR
This paper introduces the concept of irreducible dimension in quantum systems, providing a way to certify the true information processing capacity of high-dimensional quantum behaviors beyond trivial dimension bounds.
Contribution
It defines irreducible dimension and presents a witness for certifying irreducible dimension four, advancing device-independent quantum dimension certification.
Findings
Introduces the notion of irreducible dimension in quantum behaviors
Provides a witness for certifying irreducible dimension four
Highlights the difference between trivial dimension bounds and true information capacity
Abstract
The Hilbert space dimension of a quantum system is the most basic quantifier of its information content. Lower bounds on the dimension can be certified in a device-independent way, based only on observed statistics. We highlight that some such "dimension witnesses" capture only the presence of systems of some dimension, which in a sense is trivial, not the capacity of performing information processing on them, which is the point of experimental efforts to control high-dimensional systems. In order to capture this aspect, we introduce the notion of irreducible dimension of a quantum behaviour. This dimension can be certified, and we provide a witness for irreducible dimension four.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
