Upper and lower bounds for Tsallis-q entanglement measure

Abstract

Quantification of entanglement is important but very difficult task because, in general, different measures of entanglement, which have been introduced to determine the degree of entanglement, cannot be calculated easily for arbitrary mixed states. Hence, in order to have an approximation of entanglement, besides the numerical methods, a series of upper and lower bounds, which can be calculated analytically, have been introduced. In this paper using upper and lower bounds of concurrence and tangle, which are two measures of entanglement, and considering the relation between these measures and Tsallis-q entanglement (an another entanglement measure), upper and lower bounds for Tsallis-q entanglement for $$2\otimes d$$ bipartite mixed states are introduced. Then, by comparing these bounds with upper and lower bounds of concurrence and tangle, it is shown that, in wide range of parameters, the Tsallis-q entanglement bounds are tighter than the bounds of concurrence and tangle.