# Perimeter Institute Quantum Discussions

This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.

## Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

## Fault tolerance of "bad" quantum low-density parity check codes

Monday Oct 29, 2012
Speaker(s):

In my talk, I will discuss various families of quantum
low-density parity check
(LDPC) codes and their fault tolerance. Such codes yield finite code rates and
at the same time
simplify error correction and encoding due to low-weight stabilizer
generators. As an example, a large family of

## The effect of initial correlations on the evolution of quantum states

Monday Oct 15, 2012
Speaker(s):

Until fairly recently, it
was generally assumed that the initial state of a quantum system prepared for information processing was in a product state with its environment.  If this is the case,

the evolution is described by a completely positive map.  However, if the system and environment are initially correlated, or entangled, such that the so-called quantum discord is non-zero, then the

Scientific Areas:

## A generalization of Kochen-Specker sets

Monday Sep 24, 2012
Speaker(s):

I will discuss two
generalizations of Kochen-Specker (KS) sets: projective KS sets and generalized
KS sets. We will see that projective KS sets can be used to characterize all
graphs for which the chromatic number is strictly larger than the quantum
chromatic number. Here, the quantum chromatic number is defined via a nonlocal
game based on graph coloring. We will further show that from any graph with
separation between these two quantities, one can construct a classical channel

## Entropic uncertainty relations for quantum operations

Wednesday Sep 05, 2012
Speaker(s):
Scientific Areas:

## The Smooth Entropy Formalism on Operator Algebras and Applications to the Security Analysis of CV Crypto Schemes

Wednesday May 30, 2012
Speaker(s):

We discuss the extension of the smooth entropy formalism to arbitrary physical systems with no bound on the number of degrees of freedom, comparing them with already existing notions of entropy for infinite-dimensional systems.

Scientific Areas:

## The entropy power inequality for quantum systems

Wednesday May 16, 2012
Speaker(s):

When two independent analog signals, $X$ and $Y$ are added together giving $Z=X+Y$, the entropy of $Z$, $H(Z)$, is not a simple function of the entropies $H(X)$ and $H(Y)$, but rather depends on the details of $X$ and $Y$'s distributions.  Nevertheless, the entropy power inequality (EPI), which states that $e^{2H(Z)} \geq e^{2H(X)} + e^{2H(Y)}$, gives a very tight restriction on the entropy of $Z$.

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## Quantum Reed-Muller Codes and Magic State Distillation in All Prime Dimensions

Wednesday May 02, 2012
Speaker(s):

Joint work with Earl Campbell (FU-Berlin) and Hussain Anwar (UCL)   Magic state distillation is a key component of some high-threshold schemes for fault-tolerant quantum computation [1], [2]. Proposed by Bravyi and Kitaev [3] (and implicitly by Knill [4]), and improved by Reichardt [4], Magic State Distillation is a method to broaden the vocabulary of a fault-tolerant computational model, from a limited set of gates (e.g.

Scientific Areas:

## Universal Low-rank Matrix Recovery from Pauli Measurements

Wednesday Apr 04, 2012
Speaker(s):

We study the problem of reconstructing an unknown matrix M, of rank r and dimension d, using O(rd poly log d) Pauli measurements. This has applications to compressed sensing methods for quantum state tomography.  We give a solution to this problem based on the restricted isometry property (RIP), which improves on previous results using dual certificates. In particular, we show that almost all sets of O(rd log^6 d) Pauli measurements satisfy the rank-r RIP.

Scientific Areas:

## Negative Quasi-Probability Representation is a Necessary Resource for Quantum Computation

Wednesday Mar 21, 2012
Speaker(s):

Abstract The magic state model of quantum computation gives a recipe for universal quantum computation using perfect Clifford operations and repeat preparations of a noisy ancilla state. It is an open problem to determine which ancilla states enable universal quantum computation in this model. Here we show that for systems of odd dimension a necessary condition for a state to enable universal quantum computation is that it have negative representation in a particular quasi-probability representation which is a discrete analogue to the Wigner function.

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## A Quantum Information Approach to Statistical Physics

Wednesday Jan 25, 2012
Speaker(s):

I will first present a theorem based on the Decoupling Theorem of [1] which gives sufficient and necessary conditions for a quantum channel (CPTPM) being such that it yields the same output for almost all possible inputs. This theorem allows us to reproduce and generalize results oft [2,3], in which cornerstones of statistical physics are derived from first principles of quantum mechanics, in a very natural and easy way. Specifically, we express them in a way which allows to apply results about random 2-qubit interactions [4].

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## RECENT PUBLIC LECTURE

### Mario Livio: Brilliant Blunders

Speaker: Mario Livio