Fetching the paper…
Reading the bibliography…
When two independent analog signals, X and Y are added together giving Z=X+Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions.
J. Williamson, “On the algebraic problem concerning the normal forms of linear dynamical systems,” American Journal of Mathematics , vol. 58, no. 1, pp. pp. 141–163, 1936. [Online]. Available: http://www.jstor.org/stable/2371062
1936
Earlier work this paper cites.
C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal , vol. 27, pp. 379–423, 623–656, October 1948
1948
Earlier work this paper cites.
A. Stam, “Some inequalities satisfied by the quantities of information of Fisher and shannon,” Information and Control , vol. 2, no. 2, pp. 101 – 112, 1959. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0019995859903481
1959
Earlier work this paper cites.
N. Blachman, “The convolution inequality for entropy powers,” Information Theory, IEEE Transactions on , vol. 11, no. 2, pp. 267 – 271, apr 1965
1965
Earlier work this paper cites.
W. Beckner, “Inequalities in Fourier analysis,” The Annals of Mathematics , vol. 102, no. 1, pp. pp. 159–182, 1975. [Online]. Available: http://www.jstor.org/stable/1970980
1975
Earlier work this paper cites.
H. Brascamp and E. Lieb, “Best constants in Young’s inequality, its converse and its generalization to more than three functions,” Adv. in Math. , vol. 20, pp. 151–172, 1976
1976
Earlier work this paper cites.
E. H. Lieb, “Proof of an entropy conjecture of wehrl,” Comm. Math. Phys. , vol. 62, no. 1, pp. 35–41, 1978
1978
Earlier work this paper cites.
P. Vanheuverzwijn, “Generators for quasi-free completely positive semi-groups,” Annales de l’institut Henri Poincaré (A) Physique théorique , vol. 29, no. 1, pp. 123–138, 1978. [Online]. Available: http://eudml.org/doc/75994
1978
Earlier work this paper cites.
H. Spohn, “Entropy production for quantum dynamical semigroups,” J. Math. Phys. , vol. 19, no. 1227, 1978
1978
Earlier work this paper cites.
N. N. Čencov., “Statistical decision rules and optimal inference,” Transl. Math. Monographs, Amer. Math. Soc., Providence, RI , vol. 53, 1981
1981
Earlier work this paper cites.
M. H. M. Costa and T. M. Cover, “On the similarity of the entropy power inequality and the Brunn-Minkowski inequality,” IEEE Transactions on Information Theory , vol. 30, no. 6, pp. 837–839, 1984
1984
Earlier work this paper cites.
A. R. Barron, “Entropy and the central limit theorem,” Ann. Probab. , vol. 14, no. 1, pp. 336–342, 1986
1986
Earlier work this paper cites.
L. L. Campbell, “An extended Čencov characterization of the information metric,” Proceedings of the American Mathematical Society , vol. 98, no. 1, pp. 135–141, 1986
1986
Cited alongside, same era.
A. Dembo, T. Cover, and J. Thomas, “Information theoretic inequalities,” Information Theory, IEEE Transactions on , vol. 37, no. 6, pp. 1501 –1518, nov 1991
1991
Cited alongside, same era.
S. Szarek and D. Voiculescu, “Volumes of restricted minkowski sums and the free analogue of the entropy power inequality,” Communications in Mathematical Physics , vol. 178, pp. 563–570, 1996. [Online]. Available: http://dx.doi.org/10.1007/BF02108815
1996
Cited alongside, same era.
D. Petz, “Monotone metrics on matrix spaces,” Linear Algebra Appl. , vol. 244, pp. 81–96, 1996
1996
Cited alongside, same era.
R. Zamir, “A proof of the Fisher information inequality via a data processing argument,” Information Theory, IEEE Transactions on , vol. 44, no. 3, pp. 1246 –1250, may 1998
M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian quantum states,” Phys. Rev. Lett. , vol. 96, p. 080502, Mar 2006. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevLett.96.080502
2006
Later among the works it cites.
S. Guha, “Multiple-user quantum information theory for optical communication channels,” Ph.D. dissertation, MIT, Dept. of Electrical Engineering and Computer Science., 2008
2008
Later among the works it cites.
S. Guha, B. Erkmen, and J. Shapiro, “The entropy photon-number inequality and its consequences,” in Information Theory and Applications Workshop, 2008 , 2008, pp. 128–130
2008
Later among the works it cites.
A. Kagan and T. Yu, “Some inequalities related to the stam inequality,” Applications of Mathematics , vol. 53, pp. 195–205, 2008, 10.1007/s10492-008-0004-2. [Online]. Available: http://dx.doi.org/10.1007/s10492-008-0004-2
2008
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1998
Cited alongside, same era.
A. Lesniewski and M. B. Ruskai, “Monotone Riemannian metrics and relative entropy on noncommutative probability spaces,” J. Math. Phys. , vol. 40, no. 5702, 1999
1999
Cited alongside, same era.
M. J. W. Hall, “Quantum properties of classical Fisher information,” Phys. Rev. A , vol. 62, p. 012107, Jun 2000. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevA.62.012107
2000
Cited alongside, same era.
A. Holevo, M. Sohma, and O. Hirota, “Error exponents for quantum channels with constrained inputs,” Reports on Mathematical Physics , vol. 46, no. 3, pp. 343 – 358, 2000. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0034487700900053
2000
Cited alongside, same era.
V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, and J. H. Shapiro, “Minimum output entropy of bosonic channels: A conjecture,” Phys. Rev. A , vol. 70, p. 032315, Sep 2004. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevA.70.032315
2004
Cited alongside, same era.
S. Verdu and D. Guo, “A simple proof of the entropy-power inequality,” Information Theory, IEEE Transactions on , vol. 52, no. 5, pp. 2165 –2166, may 2006
2006
Cited alongside, same era.
O. Rioul, “Two proofs of the Fisher information inequality via data processing arguments,” April 2006, arXiv:cs/0604028v1
2006
Cited alongside, same era.
T. Hiroshima, “Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs,” Phys. Rev. A , vol. 73, p. 012330, Jan 2006. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevA.73.012330
2006
Cited alongside, same era.
2009
Later among the works it cites.
V. Giovannetti, A. S. Holevo, S. Lloyd, and L. Maccone, “Generalized minimal output entropy conjecturefor one-mode Gaussian channels: definitions and some exact results,” J. Phys. A , vol. 43, no. 032315, 2010
2010
Later among the works it cites.
D. Petz and C. Ghinea, “Introduction to quantum Fisher information,” 2010, arXiv:1008.2417
2010
Later among the works it cites.
——, “Information theoretic proofs of entropy power inequalities,” Information Theory, IEEE Transactions on , vol. 57, no. 1, pp. 33 –55, jan. 2011
2011
Later among the works it cites.
F. Hiai, M. Mosonyi, D. Petz, and C. Beny., “Quantum f-divergences and error correction,” 2011
2011
Later among the works it cites.
M. Raginsky, “Divergence in everything: Cramér-Rao from data processing,” Information Structuralist, blog infostructuralist.wordpress.com
2011
Later among the works it cites.
A. E. Gamal and Y.-H. Kim, Network Information Theory . Cambridge University Press, 2012
2012
Closest in time.
R. König and G. Smith, “Limits on classical communication from quantum entropy power inequalities,” Nature Photonics , vol. 7, p. 142–146, January 2013
2013
Closest in time.