# Video Library

Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres.  Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities.  Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA)PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.

## Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration

Tuesday Jul 06, 2010
Speaker(s):

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 random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument.

## Introduction to additivity problems and Hastings' counterexample

Tuesday Jul 06, 2010

## Random Quantum Repeated Interactions and Random Invariant states

Monday Jul 05, 2010
Speaker(s):

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 a convergence result for the iterations of generic channels. This allows to define a set of random quantum states called ''asymptotic induced ensemble''.

## Two random matrix problems inspired by quantum information

Monday Jul 05, 2010
Speaker(s):

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)^{otimes k}, where k and p/d^k are fixed while d grows?

## Random graph states and area laws

Monday Jul 05, 2010
Speaker(s):

We associate to any unoriented graph a random pure quantum state, obtained by randomly rotating a tensor product of Bell states.

## Ensembles of random quantum states

Monday Jul 05, 2010
Speaker(s):

## Singular values, complex eigenvalues and the single ring theorem

Monday Jul 05, 2010
Speaker(s):

Limit laws and large deviations for the empirical measure of the singular values for ensembles of non-Hermitian matrices can be obtained based on explicit distributions for the eigenvalues. When considering the eigenvalues, however, the situation changes dramatically, and explicit expressions for the joint distribution of eigenvalues are not available (except in very special cases). Nevertheless, in some situations the limit of the empirical measure of eigenvalues (as a measure supported in the complex plane) can be computed, and it exhibits interesting features.

## Some limit theorems in operator-valued noncommutative probability

Monday Jul 05, 2010
Speaker(s):

A famous result in classical probability - Hin\v{c}in's Theorem - establishes a bijection between infinitely divisible probability distributions and limits of infinitesimal triangular arrays of independent random variables. Analogues of this result have been proved by Bercovici and Pata for scalar-valued {\em free probability}. However, very little is known for the case of operator-valued distributions, when the field of scalars is replaced by a $C^*$-algebra; essentially the only result known in full generality that we are aware of is Voiculescu's operator-valued central limit theorem.

## Isotropic Entanglement

Sunday Jul 04, 2010
Speaker(s):

One of the major problems hindering progress in quantum many body systems is the inability to describe the spectrum of the Hamiltonian. The spectrum corresponds to the energy spectrum of the problem and is of out-most importance in accounting for the physical properties of the system. A perceived difficulty is the exponential growth of the Hamiltonian with the number of particles involved. Therefore, even for a modest number of particles, direct computation appears intractable.

## On the comparison of volumes of quantum states

Sunday Jul 04, 2010
Speaker(s):

Entangled (i.e., not separable) quantum states play fundamental roles in quantum information theory; therefore, it is important to know the ''size'' of entanglement (and hence separability) for various measures, such as, Hilbert-Schmidt measure, Bures measure, induced measure, and $\alpha$-measure. In this talk, I will present new comparison results of $\alpha$-measure with Bures measure and Hilbert-Schmidt measure.

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## RECENT PUBLIC LECTURE

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