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statistical mixture

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2 - Description of Quantum Systems in Terms of the Density Matrix
Claude Fabre, Sorbonne Université, Paris
With contributions by Rodrigo G. Cortiñas
Book:

Quantum Processes and Measurement

Published online:

27 July 2023

Print publication:

10 August 2023, pp 17-32
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Summary

Presents the basic postulates of quantum mechanics in terms of the density matrix instead of the usual state vector formalism in the case of an isolated system. Extends it to the case of open systems with the help of the reduced density matrix formalism, and to the case of an imperfect state preparation described by a statistical mixture. Introduces the concept of quantum state purity to characterize the degree of mixture of the state, and shows that one can always "purify" a density matrix by going into a Hilbert space of larger dimension.