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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 16:24, 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
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[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
- ↑ Taoufik Amri, Quantum behavior of measurement apparatus, arXiv:1001.3032 (2010).