Talks

One of the quintessential features of quantum information is its exclusivity, the inability of strong quantum correlations to be shared by many physical systems. Likewise, complementarity has a similar status in quantum mechanics as the sine qua non of quantum phenomena. We show that this is no coincidence, and that the central role of exclusivity in quantum information theory stems from the phenomenon of complementarity. We adopt an information-theoretic approach to complementarity, which leads to a new and simple definition of private states and new proofs of the achievable asymptotic rates of both secret key and entanglement distillation. From the latter follows a new proof of the direct part of the quantum noisy channel coding theorem.

A discussion of how the zero point energy of atoms is what makes possible their existence in our universe – atoms are purely quantum mechanical objects.
Learning Outcomes:
• Continuation of QM-9: A calculus-based derivation of the zero point energy of the quantum harmonic oscillator.
• How our previous understanding of energy quantization and zero point energy can be applied also to the hydrogen atom.
• Why classical atoms cannot exist in our universe, and how the Heisenberg Uncertainty Principle and associated zero point energy stabilizes atoms, making their existence possible.

Understanding the zero point energy of the quantum harmonic oscillator as a consequence of the Heisenberg Uncertainty Principle.
Learning Outcomes:
• Understanding why the minimum energy of a ball in a bowl must be greater than zero based on the Heisenberg Uncertainty Principle.
• How the Heisenberg Uncertainty Principle adds a purely quantum mechanical kinetic energy to the ball, in addition to its classical potential energy.
• Understanding graphically how the total energy – the sum of the classical potential energy and the new quantum kinetic energy – has a minimum that is greater than zero: the zero point energy.

A continuation of the SR-10 discussion on length contraction. Resolving Principle 2*.
Learning Outcomes:
• Relativity of simultaneity revisited – gaining a deeper understanding of what it means.
• A full understanding of the nature of length contraction based on relativity of simultaneity.
• Resolving a key paradox in special relativity: Principle 2*, introduced in SR-4. How it is possible to measure the same speed for the light whether you are running toward or away from a flashlight.

A discussion of the space and time axes of a moving observer and an introduction to length contraction.
Learning Outcomes:
• Understanding why and by how much a moving observer’s position axis is “tilted in time.”
• Understanding how a moving platform appears to a stationary observer.
• Beginning to understand the cause of length contraction.

Domains were introduced in computer science in the late 1960\'s by Dana Scott to provide a semantics for the lambda calculus (the lambda calculus is the basic prototype for a functional programming language i.e. ML). The study of domains with measurements was initiated in the speaker\'s thesis: a domain provides a qualitative view of information expressed in part by an \'information order\' and a measurement on a domain expresses a quantitative view of information with respect to the underlying qualitative aspect. The theory of domains and measurements was initially introduced to provide a first order model of computation, one in which a computation is viewed as a process that evolves in a space of informatic objects, where processes have informatic rates of change determined by the manner in which they manipulate information. There is a domain of binary channels with capacity as a measurement. There is a domain of finite probability distributions with entropy as a measurement. There is a domain of quantum mixed states with entropy as a measurement. There is a domain of spacetime intervals with global time as a measurement. In this setting, similarities between QM and GR emerge, but also some important differences. In a domain, if we write x <= y, then it means that x carries information about y, while x << y is a stronger relation that means x carries *essential* information about y. In GR, the domain theoretic relation << can be proven to be timelike causality. It possesses stronger mathematical properties than << does in QM. However, by an application of the maximum entropy principle, we can restrict the mixed states in consideration and this difference is removed: the domains of events and mixed states are both globally hyperbolic -- where globally hyperbolic is a purely order theoretic idea that just happens to coincide with the usual notion in the case of GR. Along the way, we will see domain theoretic ways of distinguishing between the Newtonian and relativistic notions of time, how to reconstruct the topology and geometry of spacetime in a purely order theoretic manner beginning from only a countable set, see that the Holevo capacity of a unital qubit channel is determined by the largest value of its informatic derivative and have reason to wonder if distance can be defined as the amount of information (capacity) that can be transmitted between two points.

Symmetry principles in physics are a very powerful guiding principle. Sometimes they are so powerful that they can determine a theory completely. This talk will be a tour from the Standard Model of particle physics to string theory compactifications using mostly symmetry arguments.

Taking our intuitive understanding of the quantum world gained by studying a particle in a one-dimensional box, we generalize to understand a quantum harmonic oscillator.
Learning Outcomes:
• Introduction to the classical physics of a ball rolling back and forth in a bowl, a simple example of a very important type of bounded motion called a “harmonic oscillator.”
• The quantization of allowed energies of a harmonic oscillator: even spacing between energy levels, and zero point energy.
• Being able to sketch the allowed wavefunctions and particle probability patterns of a quantum harmonic oscillator, including a new phenomenon called “tunnelling.”