# Mathematics Colloquia and Seminars

Entanglement is a resource in quantum information protocols, enabling quantum teleportation, for example. Many quantum protocols (such as teleportation) are implemented on a composite quantum system that is shared by two parties who are supposed to be physically separate. Thus, while each party may perform operations on her individual system, no global operations on the composite system are possible. This paradigm is known as a restriction to Local Operations and Classical Communications (LOCC). We discuss the problem of LOCC state discrimination, in which Alice and Bob's composite system is in an unknown state V from a known set $S$. Their goal is to determine the identity of V using only LOCC. Often, the set S consists of mutually orthogonal vectors, so that perfect discrimination would be possible if global operations were allowed. The remarkable range of results in this area are discussed, highlighting the role of entanglement as sometimes a hindrance, sometimes a resource. This will include recent work by the speaker on determining whether or not a composite system is in a particular state V.