Abstract
In this paper we prove several theorems about quantum mechanical entropy, in particular, that it is strongly subadditive (SSA). These theorems were announced in an earlier note,1 to which we refer the reader for a discussion of the physical significance of SSA and for a review of the historical background. We repeat here a bibliography of relevant papers.2-9.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Note
E. H. Lieb and M. B. Ruskai, Phys. Rev. Letters 30, 434 (1973).
H. Araki and E. H. Lieb, Commun. Math. Phys. 18, 160 (1970).
F. Bauman and R. Jost, in Problems of Theoretical Physics; Essays Dedicated to N. N. Bogoliubov (Moscow, Nauka, 1969), p. 285.
R. Jost, in Quanta: Essays in Theoretical Physics Dedicated to Gregor Wentzel, edited by P. G. O. Freund, C. J. Goebel and Y. Nambu (University of Chicago Press, Chicago, 1970), p. 13.
F Baumann, Helv. Phys. Acta 44, 95 (1971).
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).
E. P. Wigner and M. M. Yanase, Proc Nat. Acad. Sci. 49, 910 (1963); Can. J. Math. 16. 397(1964).
A. Uhlmann. “Endlich Dimensionale Dichtematrizen, II”. Wiss. Z. Karl-Marx-University Leipzig, Math-Naturwiss. R. 22, Jg. H.2, 139 (1973).
D. Ruelle, Statistical Mechanics: Rigorous Results (Benjamin, New York, 1969), Theorem 2.5.2.
E. H. Lieb, “Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture”, Adv. in Math., to appear Dec. 1973.
H. Epstein, Commun. Math. Phys. 37, 317 (1973).
M. B. Ruskai, “A Generalization of the Entropy Using Traces on von Neumann Algebras,” preprint.
O. Lanford III, in Statistical Mechanics and Quantum Field Theory edited by C. De Witt and R. Stora (Gordon and Breach, New York, 1971), p. 174.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lieb, E.H., Ruskai, M.B. (2002). Proof of the strong subadditivity of quantum-mechanical entropy. In: Loss, M., Ruskai, M.B. (eds) Inequalities. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55925-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-55925-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62758-3
Online ISBN: 978-3-642-55925-9
eBook Packages: Springer Book Archive