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{{technical|date=June 2012}}
 
In [[quantum mechanics]], and especially [[quantum information]] theory, the '''purity''' of a quantum state is a scalar defined as
 
:<math>\gamma \, \equiv \, \mbox{Tr}(\rho^2) \,</math>
 
where <math>\rho \,</math> is the [[density matrix]] of the state. The purity can range between unity, corresponding to a completely pure state, and <math>1/d \,</math>, corresponding to a completely mixed state. (Here, <math>d \,</math> is the [[dimension]] of the density matrix.)
 
Purity is trivially related to the [[Linear entropy]] <math>S_L \,</math> of a state by
:<math>\gamma = 1-S_L \, .</math>
 
== Projectivity of a measurement ==
 
For a quantum measurement, '''the projectivity'''<ref>Taoufik Amri, Quantum behavior of measurement apparatus, [http://arxiv1.library.cornell.edu/abs/1001.3032 arXiv:1001.3032] (2010).</ref> is the purity of its [[Quantum tomography|pre-measurement state]].
This [[Quantum tomography|pre-measurement state]] is the main tool of the [[Quantum Retrodiction|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 ==
<references/>
 
{{DEFAULTSORT:Purity (Quantum Mechanics)}}
[[Category:Quantum mechanics]]
 
 
{{quantum-stub}}

Revision as of 15:24, 30 January 2014

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

γTr(ρ2)

where ρ 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 SL of a state by

γ=1SL.

Projectivity of a measurement

For a quantum measurement, the projectivity[1] 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

  1. Taoufik Amri, Quantum behavior of measurement apparatus, arXiv:1001.3032 (2010).


Template:Quantum-stub