Quantum instrument

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

$ho^\{AB\}\; ightarrow\; ilde\{\; ho\}^\{AA\text{'}B\}\; :=\; sum\_k\; mathcal\{E\}\_kleft(\; ho^\{AB\}\; ight)otimes\; vert\; k\; angle\; langle\; kvert^\{A\text{'}\}$

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

ee also

A brief mention appears in the [http://en.wikipedia.org/wiki/Quantum_channel#Instrument] Quantum Channel] article.

References

E. Davies, J. Lewis. An operational approach to quantum probability, Comm. Math. Phys., vol. 17, pp. 239-260, 1970.

[ http://arxiv.org/abs/quant-ph/0306078v1 Distillation of secret key paper]

[ http://arxiv.org/abs/quant-ph/0501045 Another paper which uses the concept ]