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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>
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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}}

Latest revision as of 14:03, 4 December 2014


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