Lower bound on concurrence and distillation for arbitrary-dimensional bipartite quantum states

Abstract

We present a lower bound of concurrence for arbitrary-dimensional bipartite quantum states. This lower bound may be used to improve all the known lower bounds of concurrence. Moreover, the lower bound gives rise to an operational sufficient criterion of distillability of quantum entanglement. The significance of our result is illustrated by quantitative evaluation of entanglement for entangled states that fail to be identified by the usual concurrence estimation method and by showing the distillability of mixed states that cannot be recognized by other distillability criteria.

Quantifying entanglement resources

“…In the general case it is not easy to estimate C(ρ) and there is a vast literature on lower bounds of the concurrence (e.g., [87,122,123,124,125,126,127,128,129,130,131]). …”

A lower bound of concurrence for multipartite quantum systems

“…[Proof]. From the expression of concurrence (13), it is straightforward to prove that the concurrence of pure state |ϕ and the concurrence of |ϕ 2⊗2⊗2 with respect to |ϕ have the following relation,…”

Lower bound of multipartite concurrence based on sub-partite quantum systems

“…In [23]- [24], the authors presented a lower bound of concurrence by decomposing the joint Hilbert space into many 2 ⊗ 2 and s ⊗ t-dimensional subspaces, which improve all the known lower bounds of concurrence. A similar nice algorithms and progress have been made towards lower bounds of concurrence for tripartite quantum systems [25,26] and other multipartite quantum systems [27]- [28] by bipartite partitions of the whole quantum system.…”