New Inequality for Density Matrices of Single Qudit States

M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, UK (2000). E. H. Lieb and M. B. Ruskai, J. Math. Phys., 14, 1938 (1973). M. A. Nielsen and D. Petz, “A simple proof of the strong subadditivity inequality,” arXiv:quantph/ 0408130 (2005). E. A. Carlen, and E. H. Lieb, Lett. Math. Phys., 83, 107 (2008) [arXiv:0710.4167 (2007)]. E. A. Carlen and Elliott H. Lieb, “A Minkowski-type trace inequality and strong subadditivity of quantum entropy,” arXiv:math/0701352 (2007). H. Araki and E. H. Lieb, Commun. Math. Phys., 18, 160 (1970). E. A. Carlen and E. H. Lieb, Lett. Math. Phys., 101, 1 (2012). E. H. Lieb, Adv. Math., 11, 267 (1973). E. H. Lieb, Bull. Am. Math. Soc., 81, 1 (1975). M. B. Ruskai, J. Math. Phys., 43, 4358 (2002); erratum ibid 46, 019901 (2005). M. B Ruskai, Commun. Math. Phys., 26, 280 (1972). E. A. Carlen and E. H. Lieb, “Remainder terms for some quantum entropy inequalities,” arXiv:1402.3840 [quant-ph] (2014). D. W. Robinson and D. Ruelle, Commun. Math. Phys., 5, 288 (1967). O. Lanford III and D. W. Robinson, J. Math. Phys., 9, 1120 (1968). M. B. Ruskai, “Lieb’s simple proof of concavity (A,B) → TrA p K † B 1−p K and remarks on related inequalities,” arXiv:quant-ph/0404126v1 (2004). V. N. Chernega and O. V. Man’ko, J. Russ. Laser Res., 34, 383 (2013). V. N. Chernega and O. V. Man’ko, J. Russ. Laser Res., 35, 27 (2014). M. A. Man’ko and V. I. Man’ko, Phys. Scr., T160, 014030 (2014). M. A. Man’ko and V. I. Man’ko, “The maps of matrices and portrait maps of density operators of composite and noncomposite systems,” arXiv:1404.3650 [quant-ph] (2014). V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, “Minkowski-type inequality for arbitrary density matrix of composite and noncomposite systems,” arXiv:1405-4956v1 [quant-ph] (2014). V. N. Chernega and V. I. Man’ko, J. Russ. Laser Res., 28, 103 (2007). C. Lupo, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Theor., 40, 13091 (2007).