Geometric measure of mixing of quantum state

We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this expression corresponds to the squared Euclidian distance betwee...

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Main Authors:	H.P. Laba, V.M. Tkachuk
Format:	Article
Language:	English
Published:	Institute for Condensed Matter Physics 2018-09-01
Series:	Condensed Matter Physics
Subjects:	mixed states density matrix Hilbert-Schmidt distance
Online Access:	https://doi.org/10.5488/CMP.21.33003

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spelling	doaj-162a551b28954487b2b70d09b33c7a202020-11-25T01:17:21ZengInstitute for Condensed Matter PhysicsCondensed Matter Physics1607-324X2224-90792018-09-012133300310.5488/CMP.21.33003Geometric measure of mixing of quantum stateH.P. LabaV.M. TkachukWe define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this expression corresponds to the squared Euclidian distance between the mixed state and the pure one in space of eigenvalues of the density matrix. As an example, geometric measure of mixing for spin-1/2 states is calculated.https://doi.org/10.5488/CMP.21.33003mixed statesdensity matrixHilbert-Schmidt distance
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	H.P. Laba V.M. Tkachuk
spellingShingle	H.P. Laba V.M. Tkachuk Geometric measure of mixing of quantum state Condensed Matter Physics mixed states density matrix Hilbert-Schmidt distance
author_facet	H.P. Laba V.M. Tkachuk
author_sort	H.P. Laba
title	Geometric measure of mixing of quantum state
title_short	Geometric measure of mixing of quantum state
title_full	Geometric measure of mixing of quantum state
title_fullStr	Geometric measure of mixing of quantum state
title_full_unstemmed	Geometric measure of mixing of quantum state
title_sort	geometric measure of mixing of quantum state
publisher	Institute for Condensed Matter Physics
series	Condensed Matter Physics
issn	1607-324X 2224-9079
publishDate	2018-09-01
description	We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this expression corresponds to the squared Euclidian distance between the mixed state and the pure one in space of eigenvalues of the density matrix. As an example, geometric measure of mixing for spin-1/2 states is calculated.
topic	mixed states density matrix Hilbert-Schmidt distance
url	https://doi.org/10.5488/CMP.21.33003
work_keys_str_mv	AT hplaba geometricmeasureofmixingofquantumstate AT vmtkachuk geometricmeasureofmixingofquantumstate
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Geometric measure of mixing of quantum state

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