In functional analysis and quantum measurement theory, a positive-operator valued measure (POVM) is a measure whose elements are non-negative self-adjoint operators on a Hilbert space. It is the most general formulation of a measurement in the theory of quantum physics. The need for the POVM formalism arises from the fact that projective measurements on a larger system, described mathematically by a projection-valued measure (PVM), will act on a subsystem in ways that cannot be described by a PVM on the subsystem alone. They are used in the field of quantum information.
In rough analogy, a POVM is to a PVM what a density matrix is to a pure state. Density matrices can describe part of a larger system that is in a pure state (see purification of quantum state); analogously, POVMs on a physical system can describe the effect of a projective measurement performed on a larger system.
Historically, the term probability-operator measure (POM) has been used as a synonym for POVM, although this usage is now rare.
Read more about POVM: Definition, POVMs and Measurement, Post-measurement State, Neumark's Dilation Theorem, Quantum Properties of Measurements, An Example: Unambiguous Quantum State Discrimination, SIC-POVM, See Also