Entropic Inequalities for a Class of Quantum Secret Sharing States
arXiv:1009.0492 · doi:10.1103/PhysRevA.83.042303
Abstract
It is well-known that von Neumann entropy is nonmonotonic unlike Shannon entropy (which is monotonically nondecreasing). Consequently, it is difficult to relate the entropies of the subsystems of a given quantum state. In this paper, we show that if we consider quantum secret sharing states arising from a class of monotone span programs, then we can partially recover the monotonicity of entropy for the so-called unauthorized sets. Furthermore, we can show for these quantum states the entropy of the authorized sets is monotonically nonincreasing.
LaTex, 5 pages