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PERIMETER INSTITUTE RECORDED SEMINAR ARCHIVE

PIRSA:C10016 - Random Matrix Techniques in Quantum Information - 2010PODCAST Subscribe to podcast

Random Matrix Techniques in Quantum Information

Organizer(s):

Collection URL: http://pirsa.org/C10016


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PIRSA:10070012  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Ensembles of random quantum states
Speaker(s): Karol Zyczkowski
Abstract: TBA
Date: 05/07/2010 - 1:30 pm

PIRSA:10070013  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Random graph states and area laws
Speaker(s): Ion Nechita
Abstract: We associate to any unoriented graph a random pure quantum state, obtained by randomly rotating a tensor product of Bell states. Marginals of such states define new ensembles of density matrices, which we study in the asymptotical regime of large Hilbert spaces. Limit eigenvalue distributions are ... read more
Date: 05/07/2010 - 2:15 pm

PIRSA:10070014  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Two random matrix problems inspired by quantum information
Speaker(s): Andris Ambainis
Abstract: In this talk, I describe two cases in which questions in quantum information theory have lead me to random matrices. In the first case, analyzing a protocol for quantum cryptography lead us to the following question: what is the largest eigenvalue of a sum of p random product states in (C^d)^{oti... read more
Date: 05/07/2010 - 3:30 pm

PIRSA:10070015  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Random Quantum Repeated Interactions and Random Invariant states
Speaker(s): Clement Pellegrini
Abstract: Within the framework of quantum repeated interactions we investigate the large time behaviour of random quantum channel. We focus on generic quantum channels generated by unitary operators which are randomly distributed along the Haar measure. After studying the spectrum of these channels, we state ... read more
Date: 05/07/2010 - 4:15 pm

PIRSA:10070018  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Introduction to additivity problems and Hastings' counterexample
Speaker(s): Chris King
Abstract: TBA
Date: 06/07/2010 - 10:30 am

PIRSA:10070020  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration
Speaker(s): Fernando Brandao
Abstract: In 2008 Hastings reported a randomized construction of channels violating the minimum output entropy additivity conjecture. In this talk we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a rand... read more
Date: 06/07/2010 - 11:15 am

PIRSA:10070019  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Hastings' additivity counterexample and a sharp version of Dvoretzky theorem
Speaker(s): Stanislaw Szarek
Abstract: In this talk we will explain how the main step technical steps in the proofs by Hastings and Hayden-Winter of the non-additivity of the minimal output von Neumann and $p$-Renyi entropy (for any $p>1$) can be reduced to a sharp version of Dvoretzky's theorem on almost spherical sections of con... read more
Date: 06/07/2010 - 1:30 pm

PIRSA:10070021  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Random matrices and random quantum channels
Speaker(s): Benoit Collins
Abstract: In this talk I will describe how random matrix theory and free probability theory (and in particular, results of Haagerup and Thorbjornsen) can give insight into the problem of understanding all possible eigenvalues of the output of important classes of random quantum channels. I will also describe ... read more
Date: 06/07/2010 - 2:15 pm

PIRSA:10070022  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Minimum output entropy of quantum channels is hard to approximate
Speaker(s): Aram Harrow
Abstract: The headline result of this talk is that, based on plausible complexity-theoretic assumptions, many properties of quantum channels are computationally hard to approximate. These hard-to-compute properties include the minimum output entropy, the 1->p norms of channels, and their "regu... read more
Date: 06/07/2010 - 3:00 pm

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