A PRETTY GOOD MEASUREMENT FOR DISTINGUISHING QUANTUM STATES

We address the problem of extracting information from a single quantum system whose state is known to be in one of several possible states. In the generic case, it is notoriously difficult to find the optimal measurement, that is the measurement that provides the most possible information about the system's state. We consider a simple general prescription for a measurement that is typically not optimal but appears to be quite good. It seems to be particularly good when the states to be distinguished are equally likely and almost orthogonal.