Quantum instrument

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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 \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.

[edit] See Also

A brief mention appears in the [[1] Quantum Channel] article.