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 |
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| Date: | 2018 |
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| Language: | English |
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Інститут фізики конденсованих систем НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/157111 |
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| 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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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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| first_indexed |
2025-12-07T18:03:46Z |
| last_indexed |
2025-12-07T18:03:46Z |
| _version_ |
1850873612068716544 |