Date: Friday 2nd December

Who: Florian Girelli

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
The semi classical classical limit is an important problem in QG. Instead of trying to derive it from a hardcore QG theory we can try to construct it effectively: we would like to modify special relativity so that it would be compatible with a minimum length (Planck length). This should then reproduce the quantum gravitational fluctuations around the flat space-time.

I will present the theory and state to conclude what are the implications for quantum mechanics, and some possible relations with the semiclassical reference frames and the renormalization group.

Date: Tuesday 6 December

Who: Florian Girelli

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract: I will introduce the action of general relativity (in a 3 dimensional space-time) and show how to quantize it. That will lead me to introduce the spin networks, quantum states of geometry. I will show the many common features of this approach with what has been presented by Joe on knots and diagramatic representation of tensors or Carlos with the Hopf algebra structure. I will try each time to use language used in QIT to introduce the concepts. I hope to tell you by the end of the talk that 3d gravity is a state sum that actually describe the anyons stuff as introduced by Carlos….

A bit of knowledge of differential geometry would be welcome, though I will try to use tools that QIT people are familiar to.

Date: Tuesday 29 November

Who: Florian Girelli

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract:
I will first do a very sketchy description of the different approaches to QG and then present the main ideas behind loop quantum gravity, but also its main problems. One of them is simply to understand its physics… which can be done if one understands the notion of quantum reference frame. These objects appear in constrained hamiltonian systems and this tutorial will be mainly about describing classically then quantum mechanically constrained systems. I will hopefully finish by a list of things to do to have a better understanding of quantum relational physics, things that can be done in the context of QIT and which should be extremely relevant for QG.

Date: Friday 25th November

Who: Carlos Mochon

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
Given a quantum pure state chosen from a set with some a priori probabilities, what is the optimal measurement needed to correctly guess the given state? I’ll present a new solution to this long studied problem in terms of the pretty good measurement.

In fact, given any set of linearly independent states, there is a one to one map between discrimination problems involving theses states and pretty good measurements constructed out of these states. The map even has a simple expression but unfortunately only in the direction from PGMs to discrimination problems.

The talk is based on quant-ph/0506061 and will also cover some semidefinite programing, the Holevo conditions for optimal measurement, and a lengthy discussion of Alice and Bob’s marital problems.

Date: Thursday 24 November

Who: Graeme Smith

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract:
I’ll discuss two applications of concentration inequalities — one from computer science and the other from physics.

In the first case, I’ll use the Chernoff bound from the first talk to show there exist functions which use two weakly random independent variables to generate a single output which is almost perfectly random. Such functions, called extractors, are important for cryptography, derandomization, and communication complexity problems.

In the second case, I’ll introduce a concentration inequality due to Talagrand and show how it can be used to obtain fairly tight bounds on the free energy of a spin glass at high temperature.

Note: This talk will begin with a brief review of lecture I. As such, all homework must be handed in at the *beginning* of class.

Date: Tuesday 22nd November

Who: Carlos Mochon

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract:
The second talk “The mathematics of anyons” will study the same anyons of the first talk but from a mathematician’s perspective. We will introduce the ideas of algebras, coalgebras, bialgebras, and Hopf algebras with the goal of arriving at braided Hopf algebras. We shall then describe the quantum double construction and examine the quantum double of a finite group which generates the anyons of the previous lecture.

This talk will be mostly independent of the first talk, though it will draw its motivation from it. A stronger mathematical background, including familiarity with group representations, may be helpful for this talk.

No poets will be harmed in the course of this talk.

Date: Friday 18th November

Who: Joe Renes

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
Prepare & measure quantum key distribution protocols generically consist of two phases. In the first phase, signals prepared by the sender are transmitted over a quantum channel to the receiver, who measures them immediately upon arrival. In the second phase, communication over a classical channel is used to assist the parties in distilling a shared, secret key from the strings of signals sent and measurement obtained.

The distillation phase itself breaks down into a sequence of functions applied to these strings, and by working in the Neumark extension, these operations can be given a simple quantum description. Formalizing each step in the distillation process in a purely quantum-mechanical framework enables us to describe the whole enterprise as a quantum channel. From this perspective, the goal of the protocol is then to use this channel to create “virtual” entanglement between the parties. Then the monogamy of entanglement implies that classical keys reated from it are truly secret. While entanglement is not physically required, it arises virtually since to an eavesdropper the prepare and measure scheme is consistent with a protocol using actual entanglement.

For QKD schemes possessing a high degree of symmetry, which includes essentially all of the protocols studied to date, the effective quantum channel takes on an especially simple form. I’ll show how to determine the relevant symmetry operations and employ them to arrive at this description. This enables us to establish the security of a wide range of protocols. In particular, security of those based on equiangular spherical codes can easily be proven.

Date: Thursday 17 November

Who: Joe Renes

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract:
Picking up the thread from last time, this talk will explore some of the connections between knot theory and physics. In particular, our goal will be to understand how polynomial knot invariants can be thought of as partition functions for certain lattice models. Starting with Kauffman’s “abstract tensors”, which also have application to spin networks and quantum gravity, we’ll derive the Yang-Baxter equation governing them as a consequence of regular isotopy invariance. Then the connection to lattice models can be made, as solutions to the Yang-Baxter equation give rise to the lattice model partition functions for both vertex and interaction-round-a-face models. Focusing again on the Jones polynomial, a corresponding solution to the YBE will be presented, along with a direct connection to the partition function of the Potts model.

Date: Wednesday 16th November

Who: Graeme Smith

Seminar type: Tutorial Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
What is the probability that a random variable will differ significantly from its mean? If that variable is the empirical mean of a large number of i.i.d. variables, it is a basic fact from probability theory that the probability of deviations from the mean will be quite small. I will discuss this fact and its generalization to functions other than empirical means. In particular, I’ll introduce the method of bounded differences, or Martingale method, which is often useful in information theory and theoretical computer science.

In the second talk, I’ll present some applications of this method to random graphs and the extraction of randomness from weakly random sources.

The expected length of the talk is 60 minutes. I will attempt to deliver it smoothly in order to minimize large deviations from this expectation.
The previous sentence is a joke, and will seem much funnier after you’ve seen the talk.

Date: Tuesday 15th November

Who: Carlos Mochon

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room, Physics Annexe

Abstract:
There once was a positive charge
Who traveled around in a barge
He ran out of luck
when he circled a flux
and came back as a negative charge

The first talk “The physics of anyons” will introduce some exotic particles that are neither bosons or fermions. A concrete model for anyons will involve the discrete group gauge theory, which also exhibits the curious phenomenon of charge metamorphosis (as captured by the limerick).
Along the way we shall have discussions about references frames, the spin-statistics connection (also known as the Feynman belt stunt) and some good old fashioned field theory.

The talk will be at an introductory level and should be fairly accessible, though having heard of groups or SU(3) would be useful. An appreciation of poetry that rhymes “charge” with “charge” is also required.