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

Koenraad Audenaert (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:
author
organization
year
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.