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.
Much of the recent progress in understanding quantum theory has been achieved within an operational approach. Within this context quantum mechanics is viewed as a theory for making probabilistic predictions for measurement outcomes following specified preparations. However, thus far some of the essential elements of the theory Ã¢ÂÂ space, time and causal structure Ã¢ÂÂ elude such an operational formulation and are assumed to be fixed.
Over the last 10 years there has been an explosion of Ã¢ÂÂoperational reconstructionsÃ¢ÂÂ of quantum theory. This is great stuff: For, through it, we come to see the myriad ways in which the quantum formalism can be chopped into primitives and, through clever toil, brought back together to form a smooth whole. An image of an IQ-Block puzzle comes to mind, http://www.prismenfernglas.de/iqblock_e.htm. There is no doubt that this is invaluable work, particularly for our understanding of the intricate connections between so many quantum information protocols.
This talk reviews recent and on-going work, much of it joint with Howard Barnum, on the origins of the Jordan-algebraic structure of finite-dimensional quantum theory. I begin by describing a simple recipe for constructing highly symmetrical probabilistic models, and discuss the ordered linear spaces generated by such models. I then consider the situation of a probabilistic theory consisting of a symmetric monoidal *-category of finite-dimensional such models: in this context, the state and effect cones are self-dual.
What is the gravity dual of a strongly interacting state of matter at zero temperature and finite charge density? The simplest candidates are extremal black holes. The presence of charged matter in the bulk can often mean that extremal black holes are not the ground state. In this talk I will discuss the physics of a class of solutions, essentially charged neutron stars, that can be thermodynamically preferred over extremal black holes.
It is now exactly 75 years ago that John von Neumann denounced his own Hilbert space formalism: ``I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space no more.'' (sic) [1] His reason was that Hilbert space does not elucidate in any direct manner the key quantum behaviors. One year later, together with Birkhoff, they published "The logic of quantum mechanics". However, it is fair to say that this program was never successful nor does it have anything to do with logic. So what is logic?
Sage is a collection of mature open source software for mathematics, and new code, all unified into one powerful and easy-to-use package.
The mission statement of the Sage project is: "Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab."
More information is available at www.sagemath.org. I will use the Sage notebook (a web interface) to demonstrate the use of Sage for a variety of mathematical problems and comment on its design and future direction.
Modal quantum theory (MQT) is a discrete model that is similar in structure to ordinary quantum theory, but based on a finite field instead of complex amplitudes. Its interpretation involves only the "modal" concepts of possibility and impossibility rather than quantitative probabilities. Despite its very simple structure, MQT nevertheless includes many of the key features of actual quantum physics, including entanglement and nonclassical computation. In this talk we describe MQT and explore how modal and probabilistic theories are related.
We propose an operationally motivated definition of the physical equivalence of states in General Probabilistic Theories and consider the principle of the physical equivalence of pure states, which turns out to be equivalent to the symmetric structure of the state space. We further consider a principle of the decomposability with distinguishable pure states and give classification theorems of the state spaces for each principle, and derive the Bloch ball in 2 and 3 dimensional systems.
Usually, quantum theory (QT) is introduced by giving a list of abstract mathematical postulates, including the Hilbert space formalism and the Born rule. Even though the result is mathematically sound and in perfect agreement with experiment, there remains the question why this formalism is a natural choice, and how QT could possibly be modified in a consistent way. My talk is on recent work with Lluis Masanes, where we show that five simple operational axioms actually determine the formalism of QT uniquely.
We consider theories that satisfy: information causality, reversibility, local discriminability, all tight effects are measurable. A property of these theories is that binary systems (with two perfectly distinguishable states and no more) have state spaces with the shape of a unit ball (the Bloch ball) of arbitrary dimension. It turns out that for dimension different than three these systems cannot be entangled. Hence, the only theory with entanglement which satisfying the above assumptions is quantum theory.