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Interpolation between random matrices and free operators, and application to Quantum Information Theory
Multi angle
Authors : Parraud, Félix (Author of the conference)
CIRM (Publisher )
46L54 - Free probability and free operator algebras
52A22 - Random convex sets and integral geometry
60B20 - Random matrices (probabilistic aspects)
94A17 - Measures of information, entropy
CIRM (Publisher )
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Abstract :
One of the most important question in Quantum Information Theory was to figure out whether the so-called Minimum Output Entropy (MOE) was additive. In this talk I will start by defining the counter-example originally built by Belinschi, Collins and Nechita. Then I will explain how with the help of a novel strategy, we managed with Collins to compute concentration estimate on the probability that the MOE is non-additive and how it yielded some explicit bounds for the dimension of spaces where violation of the MOE occurs. Finally, I will talk more in detail about this novel strategy which consists in interpolating random matrices and free operators with the help of free stochastic calculus.
Keywords : random matrix theory; free probability theory; random set; quantum information theory
MSC Codes : Keywords : random matrix theory; free probability theory; random set; quantum information theory
46L54 - Free probability and free operator algebras
52A22 - Random convex sets and integral geometry
60B20 - Random matrices (probabilistic aspects)
94A17 - Measures of information, entropy
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 26/07/2024 Conference Date : 08/07/2024 Subseries : Research School arXiv category : Operator Algebras ; Probability ; Quantum Physics ; Mathematical Physics Mathematical Area(s) : Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:43:46 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-07-08_parraud.mp4 
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Information on the Event
Event Title : Jean Morlet Chair - Research school: Random quantum channels: entanglement and entropies / Chaire Jean Morlet - Ecole: Canaux quantiques aléatoires: Intrication et entropiesEvent Organizers : Collins, Benoît ; Demni, Nizar ; Kadri, Hachem ; Lancien, Cécilia ; Nechita, Ion ; Pellegrini, Clément Dates : 08/07/2024 - 12/07/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3051.html
Citation Data
DOI : 10.24350/CIRM.V.20200403Cite this video as: Parraud, Félix (2024). Interpolation between random matrices and free operators, and application to Quantum Information Theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20200403 URI : http://dx.doi.org/10.24350/CIRM.V.20200403 |
See Also
- [Multi angle] Strong convergence for tensor GUE random matrices / Author of the conference Yuan, Wangjun.
- [Multi angle] A Max-Flow approach to Random Tensor Networks / Author of the conference Loulidi, Faedi.
- [Multi angle] Entanglement detection in QIT: a RMT approach / Author of the conference Jivulescu, Maria.
- [Multi angle] A generic quantum Wielandt's inequality for matrix and Lie algebras / Author of the conference Capel, Angela.
Bibliography
- PARRAUD, Félix. On the operator norm of non-commutative polynomials in deterministic matrices and iid Haar unitary matrices. Probability Theory and Related Fields, 2022, vol. 182, no 3, p. 751-806. - http://dx.doi.org/10.1007/s00440-021-01101-0
- COLLINS, Benoît et PARRAUD, Félix. Concentration estimates for random subspaces of a tensor product and application to quantum information theory. Journal of Mathematical Physics, 2022, vol. 63, no 10. - https://doi.org/10.1063/5.0073837
- PARRAUD, Félix. Asymptotic expansion of smooth functions in deterministic and iid Haar unitary matrices, and application to tensor products of matrices. arXiv preprint arXiv:2302.02943, 2023. - https://doi.org/10.48550/arXiv.2302.02943
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