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In quantum mechanics, and especially quantum information theory, the purity of a quantum state is a scalar defined as

$\gamma \equiv \text{Tr}({\rho }^2)$

where $\rho$ is the density matrix of the state. The purity can range between unity, corresponding to a completely pure state, and $1/d$, corresponding to a completely mixed state. (Here, $d$ is the dimension of the density matrix.)

Purity is trivially related to the Linear entropy $S_L$ of a state by

$\gamma =1-S_L.$

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.

References

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