On a block matrix inequality quantifying the monogamy of the negativity of entanglement
 Author
 Koenraad Audenaert (UGent)
 Organization
 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.
 Keywords
 quantum information theory, negativity, block matrix, trace norm, 15A45
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU5986958
 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.
@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 = {03081087}, journal = {LINEAR \& MULTILINEAR ALGEBRA}, keyword = {quantum information theory,negativity,block matrix,trace norm,15A45}, language = {eng}, number = {12}, pages = {25262536}, 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}, }
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