Quantum Causality and Temporal Relations in Quantum Theory

In our everyday life, we experience events in a well-defined order.  This means that event A can only occur before, after or at the same time as a second event B.  It turns out that this intuition carries over through most of our scientific theories.  Even in quantum theory, where we often talk about a particle being in two places at once, scientists tend to make implicit assumptions about the order of events.  A good example of this is quantum computation.  In a quantum computer we imagine applying quantum gates to some quantum bit. While that quantum bit can be in a superposition of different states, the order in which the gates are applied is always fixed.  It wasn’t until 10-15 years ago that it was appreciated that we could also superpose the order in which gates are applied.  In other words, we can take two gates and apply them to a quantum bit in two orders at the same time.
It turns out that this can have drastic consequences for quantum information processing.  Some tasks can be done more efficiently than when the gates are applied in a fixed order, and it is also possible to do some things that cannot be done with a “normal” quantum computer.  In this project, we are interested in developing techniques to create superpositions of orders, characterize these superpositions, and then exploit them by trying to outperform standard quantum approaches.