Revisiting comparison between entanglement measures for two-qubit pure states

Ashutosh Singh, Ijaz Ahamed, Dipankar Home, Urbasi Sinha

Published 2019-07-22Version 1

Given a non-maximally entangled state, an operationally significant question is to quantitatively assess as to what extent the state is away from the maximally entangled state, which is of importance in evaluating the efficacy of the state for its various uses as a resource. It is this question which is examined in this paper for two-qubit pure entangled states in terms of different entanglement measures like Negativity(N), Logarithmic Negativity(LN) and Entanglement of Formation(EOF). Theoretical estimates show that percentage deviations from the maximally entangled state of any given entangled state, quantified by N vis-a-vis EOF, can differ quite appreciably, even up to ~15 % for states further away from the maximally entangled state, while for LN vis-a-vis EOF, the maximum value of this difference is around 23 %. This analysis is complemented by illustration of these differences in terms of empirical results obtained from a suitably planned experimental study. Thus, such appreciable amount of quantitative non-equivalence between the entanglement measures in addressing the experimentally relevant question considered in the present paper highlights the requirement of an appropriate quantifier for such intent. We indicate directions of study that can be explored towards finding such a quantifier.