A quantum instrument is a quantum operation with both classical and quantum outputs. It combines the concepts of measurement and quantum operation.

Usually it is implemented as a weighted collection of completely positive maps the sum of which is trace preserving.

Quantum Instrument: collection
acts as:


A quantum instrument is more general than a quantum operation

Quantum operation

In quantum mechanics, a quantum operation is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. This was first discussed as a general stochastic transformation for a density matrix by George Sudarshan...

because it records the outcome k of which operator acted on the state.