Quantum Physics

Physical theories ought to be built up from colloquial notions such as ’long bodies’, ’energetic sources’ etc. in terms of which one can define pre-theoretic ordering relations such as ’longer than’, ’more energetic than’. One of the questions addressed in previous work is how to make the transition from these pre-theoretic notions to quantification, such as making the transition from the ordering relation of ’longer than’ (if one body covers the other) to the notion of how much longer. In similar way we introduce dynamical notions ’more impulse’ (if in a collision one object overruns the other) and ’more energetic’ (if the effect of one source exceeds the effect of the other). In a physical model - built by coupling congruent standard actions - those basic pre-theoretic notions become measurable. We derive all (classical and relativistic) equations between basic physical quantities of Energy,  Momentum and Inertial Mass and ultimately the principle of least action.

Weak values were introduced by Aharonov, Albert, and Vaidman 25 years ago, but it is only in the last 10 years that they have begun to enter into mainstream physics. I will introduce weak values as done by AAV, but then give them a modern definition in terms of generalized measurements. I will discuss their properties and their uses in experiment. Finally I will talk about what they have to contribute to quantum foundations. 

We introduce two relative entropy quantities called the min- and max-relative 
entropies and discuss their properties and operational meanings.

These relative entropies act as parent quantities for tasks such as data compression, information
transmission and entanglement manipulation in one-shot information theory. Moreover, they lead us to define entanglement monotones which have interesting operational interpretations.

Shor's algorithm can be a meaningful test for experimental quantum processing systems, when suitably realized.  I present results from a  recent implemenation of quantum factoring using trapped ion qubits, demonstrating feed-forward control, use of quantum memory during computation, and cascaded three-qubit gates.  Such capabilities are necessary ingredients for a future large-scale,
fault-tolerant quantum computing system.

While quantum measurement remains the central philosophical conundrum of quantum mechanics, it has recently grown into a respectable (read: experimental!) discipline as well.  New perspectives on measurement have grown  out of new technological possibilities, but also out of
attempts to design systems for quantum information processing, which promise to be exponentially more powerful than any possible classical computer.  I will try to give a flavour about some of these perspectives, focussing largely on a particular paradigm known as "weak measurement."
Weak measurement is a natural extension of a pragmatic view of what it means to measure something about a quantum system, yet leads to some rather surprising results.  I will describe a few examples of our recent experiments using weak measurement to probe fundamental issues in  uantum mechanics such as what the minimum disturbance due to a quantum measurement is.  I will also argue that there are regimes in which weak measurement offers a practical advantage for sensitive measurements.