Abstract

The study of the connections between entanglement and non-classicality has seen an increasing interest in the last few years. Several forms of entanglement witnesses have been proposed to reveal and quantify the entanglement of a particular state or a particular class of states. Non-classicality indicators have been proposed so as to quantify quantum correlations in two-qubit states. It has been demonstrated that there are interesting situations in which non-entangled states (i.e. separable) can behave in a non-classical way [1]. Investigating on the interplay between quantum correlations and global state mixedness is an interesting topic. Such study is dressed with even deeper fundamental significance when extended to non-classical/not-entangled states. However, the more pragmatic aspects of such endeavors should be stressed as well, given that non-entangled states can be useful for quantum computing. In a recent paper [2] a new non-classicality indicator, named AMID, has been proposed as an “ameliorated” version of measurement induced disturbance (or MID), which was originally proposed by Luo in [1]. AMID is an improvement as it embodies a faithful estimator of non-classicality that, at contrast with MID, vanishes exactly for fully classical states. For 2-qubit mixed states, a relation exists between AMID and Quantum Discord [3] and such non-classicality indicators share the same set of extremal states in the Entropic plane [2]. The two extremal bounds (blue and black lines in Fig.1) correspond to two different families of 2-qubit mixed states. States ${\rho }^{low}(p)=(1-p)|{\varphi }^{+}〉〈{\varphi }^{+}|+p|{\varphi }^{-}〉〈{\varphi }^{-}|\left[\text{with}|{\varphi }^{+}〉=\frac{1}{\sqrt{2}}\left(|00〉+|11〉\right)\right]$ belong to the lower bound, while the upper bound is spanned by ρ^up (ε, p) = (1 −ε) |ϕ ⁺(p)〉〈ϕ ⁺(p)| +ε|01〉 〈01| [for suitable values of the parameters (ε, p) and $|{\varphi }^{+}(p)〉=\sqrt{1-p}|00〉+\sqrt{p}|11〉$].

© 2011 IEEE