Please use this identifier to cite or link to this item: https://doi.org/10.1098/rspa.2012.0737
Title: The structure of Rényi entropic inequalities
Authors: Linden, N.
Mosonyi, M.
Winter, A. 
Keywords: Entropy inequalities
Homogeneous inequalities
Multi-partite quantum states
Rényi entropies
Subadditivity
Issue Date: 8-Oct-2013
Citation: Linden, N., Mosonyi, M., Winter, A. (2013-10-08). The structure of Rényi entropic inequalities. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469 (2158) : -. ScholarBank@NUS Repository. https://doi.org/10.1098/rspa.2012.0737
Abstract: We investigate the universal inequalities relating the α-Rényi entropies of the marginals of a multipartite quantum state. This is in analogy to the same question for the Shannon and von Neumann entropies (α =1), which are known to satisfy several non-trivial inequalities such as strong subadditivity. Somewhat surprisingly, we find for 0 < α < 1 that the only inequality is non-negativity: in other words, any collection of non-negative numbers assigned to the non-empty subsets of n parties can be arbitrarily well approximated by the α-entropies of the 2n α 1 marginals of a quantum state. For α >1, we show analogously that there are no non-trivial homogeneous (in particular, no linear) inequalities. On the other hand, it is known that there are further, nonlinear and indeed non-homogeneous, inequalities delimiting the α-entropies of a general quantum state. Finally, we also treat the case of Rényi entropies restricted to classical states (i.e. probability distributions), which, in addition to non-negativity, are also subject to monotonicity. For α ≠ 0, 1, we show that this is the only other homogeneous relation. © 2013 The Author(s).
Source Title: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
URI: http://scholarbank.nus.edu.sg/handle/10635/116647
ISSN: 13645021
DOI: 10.1098/rspa.2012.0737
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

14
checked on Dec 12, 2018

WEB OF SCIENCETM
Citations

10
checked on Dec 12, 2018

Page view(s)

39
checked on Dec 14, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.