Quantum instrument
In physics, a quantum instrument is a mathematical abstraction of a quantum measurement, capturing both the classical and quantum outputs. It combines the concepts of measurement and quantum operation. It can be equivalently understood as a quantum channel that takes as input a quantum system and has as its output two systems: a classical system containing the outcome of the measurement and a quantum system containing the post-measurement state.
Definition
Let be a countable set describing the outcomes of a measurement, and let denote a collection of trace-non-increasing completely positive maps, such that the sum of all is trace-preserving, i.e. for all positive operators .
Now for describing a quantum measurement by an instrument , the maps are used to model the mapping from an input state to the output state of a measurement conditioned on a classical measurement outcome . Therefore, the probability of measuring a specific outcome on a state is given by
The state after a measurement with the specific outcome is given by
If the measurement outcomes are recorded in a classical register, whose states are modeled by a set of orthonormal projections , then the action of an instrument is given by a quantum channel with
Here and are the Hilbert spaces corresponding to the input and the output systems of the instrument.
A quantum instrument is an example of a quantum operation in which an "outcome" indicating which operator acted on the state is recorded in a classical register. An expanded development of quantum instruments is given in quantum channel.
References
![]() | This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (July 2009) |
- E. Davies, J. Lewis. An operational approach to quantum probability, Comm. Math. Phys., vol. 17, pp. 239–260, 1970.
- Distillation of secret key paper
- Another paper which uses the concept
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