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In [[physics]], a '''quantum instrument''' is a mathematical abstraction of a [[quantum measurement]], capturing both the [[classical physics|classical]] and [[quantum physics|quantum]] outputs. It combines the concepts of [[measurement]] and [[quantum operation]].
 
==Definition==
Quantum instruments are usually defined as a weighted collection of [[completely positive]] maps, the sum of which is trace preserving. That is, it is a collection <math>\mathcal{E}_k</math> of operators that act as
 
:<math>
\rho^{AB} \rightarrow
\tilde{\rho}^{AA'B} := \sum_k \mathcal{E}_k
\left( \rho^{AB} \right)\otimes \vert k \rangle \langle k\vert^{A'}
</math>
 
A quantum instrument is more general than a [[quantum operation]] because it records the outcome ''k'' of which operator acted on the state. An expanded development of quanum instruments is given in [[quantum channel]].
 
== References ==
{{No footnotes|date=July 2009}}
* E. Davies, J. Lewis. An operational approach to quantum probability, Comm. Math. Phys., vol. 17, pp.&nbsp;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]
 
{{DEFAULTSORT:Quantum Instrument}}
[[Category:Quantum mechanics]]
{{physics-stub}}

Latest revision as of 10:48, 28 October 2014

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