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A matrix convexity approach to some celebrated quantum inequalities
 Proc. Nat. Acad. Sci. USA
"... Dedicated to Gert Pedersen, who is missed for both his brilliance and his exuberant sense of humor. Abstract. Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the HansenPedersenJensen inequalities. A general argument is given using matrix p ..."
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Cited by 26 (2 self)
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Dedicated to Gert Pedersen, who is missed for both his brilliance and his exuberant sense of humor. Abstract. Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the HansenPedersenJensen inequalities. A general argument is given using matrix perspectives of operator convex functions. A matrix analogue of Maréchal’s extended perspectives provides additional inequalities, including a p + q ≤ 1 result of Lieb. 1.
Remarks on Kim’s strong subadditivity matrix inequality: extensions and equality conditions
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ACKNOWLEDGEMENTS
, 2006
"... I am deeply indebted to my advisor, Dr. David S. Citrin, for giving me the opportunity to work in this area, for his precious advice, continuous encouragement and full support, for the time and energy he devoted in discussing my research. I am also very grateful to Drs. Stephen E. Ralph and Douglas ..."
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I am deeply indebted to my advisor, Dr. David S. Citrin, for giving me the opportunity to work in this area, for his precious advice, continuous encouragement and full support, for the time and energy he devoted in discussing my research. I am also very grateful to Drs. Stephen E. Ralph and Douglas R. Denison for their assistance and valuable discussion in my research and for serving on my committee. I would like to express my sincere appreciation to Drs. Gregory D. Durgin and ShyhChiang Shen for their kindness and willingness to serve on my committee. I would also like to extend my sincere thanks to all our group members who have helped me. Finally, I would like to thank my wife, Eun Ae Lee and my son, Sehyun Kim, most heartily for their patience, encouragement, and understanding during the course of this work. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS............................................................................................. iii LIST OF TABLES.......................................................................................................... vii
NEW PERSPECTIVES AND SOME CELEBRATED QUANTUM INEQUALITIES
, 802
"... Dedicated to Gert Pedersen, whose roguish and irrepressible wit is missed by all. Abstract. Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the HansenPedersenJensen inequality. A general argument is given in terms of the matrix perspective ..."
Abstract
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Dedicated to Gert Pedersen, whose roguish and irrepressible wit is missed by all. Abstract. Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the HansenPedersenJensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function. A matrix analogue of Maréchal’s extended perspectives provides additional inequalities, including a p + q ≤ 1 result of Lieb. 1.
PERHAPS THE SIMPLEST PROOFS OF THE LIEB AND LINDBLAD JOINT CONVEXITY INEQUALITIES, AND
, 802
"... Abstract. Several important noncommutative inequalities are proved by using Hansen and Pedersen’s Jensen inequality. This approach is also used to demonstrate a matrix analogue of Maréchal’s generalized perspective construction for convex functions. 1. ..."
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Abstract. Several important noncommutative inequalities are proved by using Hansen and Pedersen’s Jensen inequality. This approach is also used to demonstrate a matrix analogue of Maréchal’s generalized perspective construction for convex functions. 1.
Preprint typeset in JHEP style HYPER VERSION arXiv:0704.3719 [hepth]
, 704
"... A holographic proof of the strong subadditivity of entanglement entropy ..."
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