Quantum field theory (QFT) is a causal theory, as evident from the Heisenberg picture. In the Schrödinger picture, however, the causality and locality is not so apparent. Typical states such as single-particle states have infinite tails in space, meaning that they cannot be generated on demand by an experimentalist.
In quantum information technology, it is crucial to be able to generate signals on demand in order to describe transfer of information. Since single photons cannot be generated on demand, we need to approximate them by strictly localized photon states. In quantum field theory, states are strictly localized to a region X in spacetime if the expectation value of any local observable outside X is equal to that in vacuum.
There are many interesting projects to consider (see below for a few). The work will involve mathematical analysis (pen-and-paper), possibly with some analytical computer tools and/or numerics. A postdoc, PhD student, and the supervisor will be involved.
Possible master's thesis topics include:
- Local measurements and operations in QFT. What exactly are local measurements and quantum operations in QFT? What is the state-update rule post measurement in QFT? How to settle Sorkin's scenario?
- Local equivalence: two states are said to be locally equivalent in X, if they predict the same measurement statistics for all local measurements in X. Develop the theory of equivalence for (possibly mixed) states, and consider the relation to explicitly time-dependent processes.
- Characterize all strictly localized states, e.g., states close to single particles.