“Quantum instrument”的意思、由来-开放百科全书

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Quantum instrument

释义

Definition
References

{{Use American English|date=January 2019}}{{Short description|Mathematical abstraction of quantum measurement
}}

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

E. Davies, J. Lewis. An operational approach to quantum probability, Comm. Math. Phys., vol. 17, pp. 239–260, 1970.
[https://arxiv.org/abs/quant-ph/0306078v1 Distillation of secret key paper]
[https://arxiv.org/abs/quant-ph/0501045 Another paper which uses the concept]

1 : Quantum mechanics

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