POVM

Summary

A POVM, or positive operator-valued measure, is the most general description of the outcome statistics of a quantum measurement. It assigns to each set of outcomes a positive operator, and the operator of the set of all outcomes is the identity. In a state $\rho$, the probability of a set of outcomes is the trace of $\rho$ times its operator. It generalizes a projection-valued measure, which describes the measurement of a self-adjoint observable. By Naimark's dilation theorem, every POVM is a projective measurement on a larger system.