Authors : ... (Author of the conference)
... (Publisher )
Abstract :
The main question that we will investigate in this talk is: what does the spectrum of a quantum channel typically looks like? We will see that a wide class of random quantum channels generically exhibit a large spectral gap between their first and second largest eigenvalues. This is in close analogy with what is observed classically, i.e. for the spectral gap of transition matrices associated to random graphs. In both the classical and quantum settings, results of this kind are interesting because they provide examples of so-called expanders, i.e. dynamics that are converging fast to equilibrium despite their low connectivity. We will also present implications in terms of typical decay of correlations in 1D many-body quantum systems. If time allows, we will say a few words about ongoing investigations of the full spectral distribution of random quantum channels. This talk will be based on: arXiv:1906.11682 (with D. Perez-Garcia), arXiv:2302.07772 (with P. Youssef) and arXiv:2311.12368 (with P. Oliveira Santos and P. Youssef).
Keywords : random matrices and tensors; quantum information; quantum condensed matter physics
MSC Codes :
60B20
- Random matrices (probabilistic aspects)
15B52
- Random matrices
81P45
- Quantum information, communication, networks
81P47
- Quantum channels, fidelity
Language : English
Available date : 26/06/2024
Conference Date : 06/06/2024
Subseries : Research talks
arXiv category : Quantum Physics ; Mathematical Physics ; Probability
Mathematical Area(s) : Analysis and its Applications ; Mathematical Physics ; Probability & Statistics
Format : MP4 (.mp4) - HD
Video Time : 00:45:06
Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
Download : https://videos.cirm-math.fr/2024-06-06_Lancien.mp4
|
Event Title : Mathematical aspects of the physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints Dates : 03/06/2024 - 07/06/2024
Event Year : 2024
Event URL : https://conferences.cirm-math.fr/2971.html
DOI : 10.24350/CIRM.V.20188403
Cite this video as:
(2024). Spectrum of random quantum channels. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20188403
URI : http://dx.doi.org/10.24350/CIRM.V.20188403
|
See Also
Bibliography
- LANCIEN, Cécilia, SANTOS, Patrick Oliveira, et YOUSSEF, Pierre. Limiting spectral distribution of random self-adjoint quantum channels. arXiv preprint arXiv:2311.12368, 2023. - https://doi.org/10.48550/arXiv.2311.12368