Summer projects

Summer projects

Sorry but we are not considering applications for summer 2017.

We offer summer research projects for interested and motivated undergraduate students. One possible project is listed below, please contact us for more information about working with our group.

Optimal quantum measurements

Optimal quantum measurements

Measurement is central to any physical theory, as it is the way in which we, as observers, find out about the world around us. Although classically it is convenient to think about measurements as revealing some pre-existing property of the system being measured, in quantum theory measurement is not a passive, but rather an active process. Measurement outcomes are probabilistic, and further, the state of the system being observed is changed as a result of measurement. An inevitable consequence of this, embodied in Heisenberg’s Uncertainty Principle, is that measurement cannot give complete information about the state of a quantum system. Understanding the limits imposed on measurement by the laws of quantum mechanics is not only of theoretical interest but also has numerous applications in quantum information and quantum metrology.

In the problem of quantum state discrimination [1] we are provided with a system prepared in one of a number of possible states. The goal is to make a measurement on the system to determine which state was actually prepared. This scenario is relevant to understanding eavesdropper attacks in quantum cryptography; more generally in decoding information in any quantum communication scheme; and in quantifying the probability of success of quantum algorithms. This project will study optimal quantum measurements for state discrimination. A number of strategies exist, each optimizing a different figure of merit. Remarkably, by allowing our measurement to sometimes fail to identify a state, a lower rate of error can be achieved in cases where the measurement succeeds. Possible directions for this project include: constructing strategies that are allowed a fixed rate of failure [2]; investigating measurement strategies in the case in which more than one copy of the state is provided [3]. The project will provide an introduction to quantum information, and in particular generalized quantum measurements. It will be mainly theoretical, with the possibility of some numerical calculations.

[1] Quantum state discrimination, S. M. Barnett and S. Croke, Advances in Optics and Photonics 1, 238 (2009).

[2] Strategies for discriminating between non-orthogonal quantum states, A. Chefles and S. M. Barnett, Journal of Modern Optics 45, 1295 (1998).

[3] Quantum data gathering, R. Blume-Kohout, S. Croke and M. Zwolak, Scientific Reports 3, 1800 (2013).