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 betw...

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Published in:Condensed Matter Physics
Date:2018
Main Authors: Laba, H.P., Tkachuk, V.M.
Format: Article
Language:English
Published: Інститут фізики конденсованих систем НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/157111
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Geometric measure of mixing of quantum state / H.P. Laba, V.M. Tkachuk // Condensed Matter Physics. — 2018. — Т. 21, № 3. — С. 33003: 1–4. — Бібліогр.: 7 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-157111
record_format dspace
spelling Laba, H.P.
Tkachuk, V.M.
2019-06-19T15:10:29Z
2019-06-19T15:10:29Z
2018
Geometric measure of mixing of quantum state / H.P. Laba, V.M. Tkachuk // Condensed Matter Physics. — 2018. — Т. 21, № 3. — С. 33003: 1–4. — Бібліогр.: 7 назв. — англ.
1607-324X
PACS: 03.65.-w, 03.67.-a
DOI:10.5488/CMP.21.33003
arXiv:1809.09469
https://nasplib.isofts.kiev.ua/handle/123456789/157111
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.
Ми означаємо геометричну мiру змiшаностi квантоваго стану як мiнiмальну вiдстань Гiльберта-Шмiдта мiж змiшаним станом та набором чистих станiв. Отримано явний вираз для геометричної мiри змiшаностi. Цiкавим є те, що цей вираз вiдповiдає квадрату евклiдової вiдстанi мiж змiшаним та чистим станами у просторi власних значень матрицi густини. Як приклад, обчислено геометричну мiру змiшаностi станiв спiна 1/2.
We thank the Members of Editorial Board for the invitation to present our results in a special issue of Condensed Matter Physics dedicated to Prof. Stasyuk’s 80th birthday. I (VMT) have known Prof. Stasyuk since 1978 when he delivered the lectures on Green’s function method for students of theoretical physics department. The lectures were very interesting and I thank Prof. Stasyuk for that. We wish Prof. Stasyuk long scientific life and bright ideas in the future.
en
Інститут фізики конденсованих систем НАН України
Condensed Matter Physics
Geometric measure of mixing of quantum state
Геометрична мiра змiшаностi квантового стану
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Geometric measure of mixing of quantum state
spellingShingle Geometric measure of mixing of quantum state
Laba, H.P.
Tkachuk, V.M.
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
author Laba, H.P.
Tkachuk, V.M.
author_facet Laba, H.P.
Tkachuk, V.M.
publishDate 2018
language English
container_title Condensed Matter Physics
publisher Інститут фізики конденсованих систем НАН України
format Article
title_alt Геометрична мiра змiшаностi квантового стану
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. Ми означаємо геометричну мiру змiшаностi квантоваго стану як мiнiмальну вiдстань Гiльберта-Шмiдта мiж змiшаним станом та набором чистих станiв. Отримано явний вираз для геометричної мiри змiшаностi. Цiкавим є те, що цей вираз вiдповiдає квадрату евклiдової вiдстанi мiж змiшаним та чистим станами у просторi власних значень матрицi густини. Як приклад, обчислено геометричну мiру змiшаностi станiв спiна 1/2.
issn 1607-324X
url https://nasplib.isofts.kiev.ua/handle/123456789/157111
citation_txt Geometric measure of mixing of quantum state / H.P. Laba, V.M. Tkachuk // Condensed Matter Physics. — 2018. — Т. 21, № 3. — С. 33003: 1–4. — Бібліогр.: 7 назв. — англ.
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