# Quantum instrument

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

## Description

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

Quantum Instrument: collection $\mathcal{E}_k$ acts as: $\rho^{AB} \rightarrow \tilde{\rho}^{AA'B} := \sum_k \mathcal{E}_k \left( \rho^{AB} \right)\otimes \vert k \rangle \langle k\vert^{A'}$

A quantum instrument is more general than a quantum operation because it records the outcome k of which operator acted on the state.