Quantum Measurement and Verification

When we measure a quantum system, it collapses it into one of several different states.  This means that each measurement we make only gives us a little bit of information about the pre-measurement state.  Thus, if we want to find out the state of some unknown quantum system, we must prepare many identical copies of that system and measure each one.  It turns out that this problem is very difficult: as the system gets larger the number of measurements that we must perform to learn the state grows exponentially.  In this research project we are interested in finding new and efficient ways to extract information from quantum systems.  This is an interesting question both for fundamental and practical reasons. Fundamentally, it is related to the projection postulate, one of the basic postulates of quantum theory.  In practice, as increasingly complex quantum systems are prepared (whether in a research lab, or as part of a quantum computer) scientists need to verify that they have in fact made that quantum state.