The seminar of the LIQ takes place on fridays at 11h00 in the seminar room opposite room N.4.217 -- that is: at the end of the corridor N on the fourth floor of building NO on the La Plaine campus of the ULB. You can find maps of the ULB campus here.
The seminar does not run every week; more like once or twice a month. If you would like to be notified of future seminars send an email to email@example.com. If you want to give a talk in the seminar, the address is the same.
7 September 2012
Manas Patra Probing the reality of quantum state
Is the quantum state real - a property of the system it is assigned to? Or does it represent only our (incomplete) knowledge of the system? It is possible that the second alternative – the epistemic character of the quantum state - comes about because quantum mechanics is obtained by some statistical averaging over a “complete” theory of nature. Such models are often called “hidden variable” models, because the true variables describing the system, the ontic state, are not accessible.
Recently Pusey, Barrett and Rudolph (1) showed that, assuming the natural assumption of “preparation independence”, epistemic models of the quantum state are in contradiction with the predictions of quantum theory. “Preparation independence” means that independent preparations of systems correspond to a joint distribution (over the ontic states) is the product of individual distributions.
Here we adopt a different approach. We show that, assuming both a form of continuity and separability (a weak form of preparation independence), epistemic interpretations of the quantum state are in contradiction with quantum theory. We also discuss some implications of “hidden- variable” models for cryptography.
We then describe a simple high-precision experiment optics experiment that tests some of the predictions of continuous and separable epistemic models. The experiment is particularly simple. It involves attenuated coherent states in time bins of dimension up to 80 propagating in optical fibres. Our experimental results are in agreement with the predictions of quantum theory and provide strong constraints on possible epistemic extensions of quantum mechanics. These results are reported in (2).
- M. F. Pusey, J. Barrett, and T. Rudolph, On the reality of the quantum state, Nature Physics, 2309, (2012).
- M. K. Patra, L. Olislager, F. Duport, J. Safioui, S. Pironio and S. Massar, Experimentally probing the reality of the quantum state, submitted (2012)
4 May 2012
Ross Duncan Non-locality in Categorical Quantum Mechanics
Mermin's argument is an important thought experiment which shows that local hidden variable models are inconsistent with the predictions of quantum theory. Unlike Bell's theorem, Mermin's argument does not rely on probabilities, but describes an experiment where certain outcomes are possible in quantum theory and impossible in any local hidden variable theory.
In this talk I'll show how Mermin's argument can be formalised in categorical quantum mechanics. We will see that the possibility of a Mermin-style non-locality argument is equivalent to the existence of strongly complementary observables -- that is, pairs of observables which jointly form a Hopf algebra. As a result, we show how to extend Mermin's argument to any theory -- quantum or otherwise -- which admits strongly complementary observables.
23 March 2012
Ross Duncan (ULB) Categorial Quantum Mechanics pt2. : picturing the one-way model of quantum computing
In the second part of this series I will present an application of the categorical approach to quantum computation, namely the question of verifying quantum algorithms for the one-way quantum computer. The one-way model is based on measuring (and thus consuming) a large array of previously entangled qubits. The order and choice of the measurements determine what algorithm is carried out. Since measurement is the key ingredient, it is not obvious that a given computation can be carried deterministically. This is the question that I'll focus on.
In this talk I will: introduce the basics of the one-way model; show how to represent quantum circuits and one-way programs in the graphical language called the zx-calculus; demonstrate how the algebraic structures discussed last time give rise to rewrite rules for the one-way programs; and, in particular, show that when the one-way program has a graph theoretic property called generalised flow, then the hopf algebra structure of the zx-calculus allows the program to be transformed into an equivalent circuit. All of this will be done by simple, local rewrites of pictures.
Despite this being the second lecture, I will be as self-contained as possible, so no need to remember anything from the last one!
16 February 2012
Ross Duncan (ULB) Categorical Quantum Mechanics pt.1
What happens to quantum theory when you throw away the Hilbert space? In particular, can one still do quantum computation without Hilbert spaces? Categorical quantum mechanics is an attempt to answer this question, by reconstituting quantum theory on the basis of the simplest mathematical structures feasible, namely monoidal categories. A great deal of quantum computation can still be carried out in a framework vastly more abstract than the usual quantum formalism, and even better, it is actually easier to do so. Aside from mathematical curiosity, there are two prime motivations for this work: firstly, by reconstructing quantum mechanics from primitive algebraic pieces we can see how and where quantum mechanics differs from other "quantum-like" theories, such as local hidden variable models and generalised probabilistic theories. Secondly: since categorical quantum mechanics is based on monoidal categories, it admits a graphical notation which can greatly simplify many calculations.
In this talk, intended to be the first of a series, I'll talk about the motivations for this work, introduce dagger-compact categories and the graphical notation, and describe the role of Frobenius and Hopf algebras as the representatives of quantum observables. I'll also demonstrate how to represent quantum circuits and perform simple calculations within the diagrammatic language.
This talk is intended to be the first of three. Future installments will focus on measurement-based quantum computation, and Mermin-style non-locality arguments.