Quantum measurement and learning

Quantum information science has demonstrated conclusively that encoding and manipulating information in quantum states can offer distinct advantages over classical information processing. Learning about a quantum system however, is still widely considered to be a classical process – a measurement is made on the system, yielding some classical information, and disturbing the state in the process. Indeed what does it mean for a quantum device to learn about the state of an external quantum system? At its most fundamental, measurement is any process by which an observer or apparatus gains information through interaction with an external system. In this talk I will discuss measurement in quantum theory, from the textbook description of measurement of an observable, to generalised measurements used in quantum information theory, to finally a generalization of the notion of measurement in quantum theory, allowing the measuring device to itself be a quantum system, gaining quantum information. I will discuss the implications of such a generalization, with reference to applications to learning about an unknown multi-partite quantum state, and to quantum adaptive algorithms.