### On a block matrix inequality quantifying the monogamy of the negativity of entanglement

(2015) LINEAR & MULTILINEAR ALGEBRA. 63(12). p.2526-2536- abstract
- We convert a conjectured inequality from quantum information theory, due to He and Vidal, into a block matrix inequality and prove a very special case. Given n matrices Ai, i = 1,..., n, of the same size, let Z1 and Z2 be the block matrices Z1 := ( A j A* i) n i, j= 1 and Z2 := ( A* j Ai) n i, j= 1, respectively. Then, the conjectured inequality is (|| Z1|| 1 - Tr Z1) 2 + (|| Z2|| 1 - Tr Z2) 2 =.. ( i ) = j || Ai || 2|| A j || 2.. 2, where || . || 1 and || . || 2 denote the trace norm and the Hilbert- Schmidt norm, respectively. We prove this inequality for the already challenging case n = 2 with A1 = I.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-5986958

- author
- Koenraad Audenaert
- organization
- year
- 2015
- type
- journalArticle (original)
- publication status
- published
- subject
- keyword
- quantum information theory, negativity, block matrix, trace norm, 15A45
- journal title
- LINEAR & MULTILINEAR ALGEBRA
- Linear Multilinear Algebra
- volume
- 63
- issue
- 12
- pages
- 2526 - 2536
- Web of Science type
- Article
- Web of Science id
- 000361996200015
- JCR category
- MATHEMATICS
- JCR impact factor
- 0.761 (2015)
- JCR rank
- 104/312 (2015)
- JCR quartile
- 2 (2015)
- ISSN
- 0308-1087
- DOI
- 10.1080/03081087.2015.1024193
- language
- English
- UGent publication?
- yes
- classification
- A1
- copyright statement
*I have transferred the copyright for this publication to the publisher*- id
- 5986958
- handle
- http://hdl.handle.net/1854/LU-5986958
- date created
- 2015-06-09 11:59:40
- date last changed
- 2017-03-27 11:15:33

@article{5986958, abstract = {We convert a conjectured inequality from quantum information theory, due to He and Vidal, into a block matrix inequality and prove a very special case. Given n matrices Ai, i = 1,..., n, of the same size, let Z1 and Z2 be the block matrices Z1 := ( A j A* i) n i, j= 1 and Z2 := ( A* j Ai) n i, j= 1, respectively. Then, the conjectured inequality is (|| Z1|| 1 - Tr Z1) 2 + (|| Z2|| 1 - Tr Z2) 2 =.. ( i ) = j || Ai || 2|| A j || 2.. 2, where || . || 1 and || . || 2 denote the trace norm and the Hilbert- Schmidt norm, respectively. We prove this inequality for the already challenging case n = 2 with A1 = I.}, author = {Audenaert, Koenraad}, issn = {0308-1087}, journal = {LINEAR \& MULTILINEAR ALGEBRA}, keyword = {quantum information theory,negativity,block matrix,trace norm,15A45}, language = {eng}, number = {12}, pages = {2526--2536}, title = {On a block matrix inequality quantifying the monogamy of the negativity of entanglement}, url = {http://dx.doi.org/10.1080/03081087.2015.1024193}, volume = {63}, year = {2015}, }

- Chicago
- Audenaert, Koenraad. 2015. “On a Block Matrix Inequality Quantifying the Monogamy of the Negativity of Entanglement.”
*Linear & Multilinear Algebra*63 (12): 2526–2536. - APA
- Audenaert, Koenraad. (2015). On a block matrix inequality quantifying the monogamy of the negativity of entanglement.
*LINEAR & MULTILINEAR ALGEBRA*,*63*(12), 2526–2536. - Vancouver
- 1.Audenaert K. On a block matrix inequality quantifying the monogamy of the negativity of entanglement. LINEAR & MULTILINEAR ALGEBRA. 2015;63(12):2526–36.
- MLA
- Audenaert, Koenraad. “On a Block Matrix Inequality Quantifying the Monogamy of the Negativity of Entanglement.”
*LINEAR & MULTILINEAR ALGEBRA*63.12 (2015): 2526–2536. Print.