Purity (quantum mechanics)
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where is the density matrix of the state. The purity can range between unity, corresponding to a completely pure state, and , corresponding to a completely mixed state. (Here, is the dimension of the density matrix.)
Purity is trivially related to the Linear entropy of a state by
Projectivity of a measurement
For a quantum measurement, the projectivity is the purity of its pre-measurement state. This pre-measurement state is the main tool of the retrodictive approach of quantum physics, in which we make predictions about state preparations leading to a given measurement result. It allows us to determine in which kind of states the measured system was prepared for leading to such a result.
- Taoufik Amri, Quantum behavior of measurement apparatus, arXiv:1001.3032 (2010).
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