What is "povm"

In functional analysis and quantum measurement theory, a positive-operator valued measure (POVM) is a measure whose values are non-negative self-adjoint operators on a Hilbert space, and whose integral is the identity operator. 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, by which we mean measurements that are performed 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. POVMs 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 are needed to specify the state of a subsystem of a larger system, even when the larger system is in a pure state (see purification of quantum state); analogously, POVMs on a physical system are used to 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.