Quantum state discrimination is a fundamental problem in quantum
mechanics underlying several applications in quantum information theory
including quantum cryptography and quantum algorithms. The problem can be
understood as follows: Suppose a quantum system has been prepared in one of
several known quantum states. We do not know which state the system is in but
wish to identify it as well as possible by performing a quantum measurement on
the system. In other words, we want to reliably distinguish quantum states, in
one of which a system has been prepared, from one another. For orthogonal
states the solution is straightforward and the states can be distinguished
perfectly, that is, without error. However, quantum mechanics forbids perfect
discrimination if the states are not mutually orthogonal.
We will first state the problem with full generality, and give examples to illustrate the non-trivial nature of a seemingly innocuous problem. We will then introduce the paradigm of local operations and classical communication (LOCC) and define quantum state discrimination problem by LOCC. We will give a brief overview of this exciting field which gives rise to new kind of nonlocality and the concept of locally hidden information.
We will also briefly discuss applications in the field of quantum cryptography.