Quantum Information

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.  

Expressions of several information theoretic quantities involve an optimization over auxiliary quantum registers. Entanglement-assisted version of some classical communication problems provides examples of such expressions. Evaluating these expressions requires bounds on the dimension of these auxiliary registers. In the classical case such a bound can usually be obtained based on the
Caratheodory theorem, but we know almost no method to bound the dimension of auxiliary quantum registers. In this talk to compare the classical and quantum sides of the problem the notion of “quantum convexification” will be defined. It will be shown that quantum convexification is strictly richer that the usual classical convexification. Moreover some techniques will be discussed which might be useful for bounding the dimension of quantum auxiliary registers.