Asymptotic Compatibility between LOCC Conversion and Recovery

TL;DR

This paper characterizes when bipartite pure entangled states can be reversibly converted via LOCC in the asymptotic limit, revealing new conditions, methods to overcome irreversibility, and insights into entanglement resource theory.

Contribution

It provides the necessary and sufficient conditions for asymptotic LOCC reversibility between pure states and introduces methods to overcome irreversibility, expanding understanding of entanglement conversion.

Findings

Reversibility conditions depend on state properties.

Perfect conversion achievable with local unitaries under certain conditions.

Far-from-maximally entangled states can serve as universal resources.

Abstract

Recently, entanglement concentration was explicitly shown to be irreversible. However, it is still not clear what kind of states can be reversibly converted in the asymptotic setting by LOCC when neither the initial nor the target state is maximally entangled. We derive the necessary and sufficient condition for the reversibility of LOCC conversions between two bipartite pure entangled states in the asymptotic setting. In addition, we show that conversion can be achieved perfectly with only local unitary operation under such condition except for special cases. Interestingly, our result implies that an error-free reversible conversion is asymptotically possible even between states whose copies can never be locally unitarily equivalent with any finite numbers of copies, although such a conversion is impossible in the finite setting. In fact, we show such an example. Moreover, we establish how to overcome the irreversibility of LOCC conversion in two ways. As for the first method, we evaluate how many copies of the initial state is to be lost to overcome the irreversibility of LOCC conversion. The second method is to add a supplementary state appropriately, which also works for LU conversion unlike the first method. Especially, for the qubit system, any non-maximally pure entangled state can be a universal resource for the asymptotic reversibility when copies of the state is sufficiently many. More interestingly, our analysis implies that far-from-maximally entangled states can be better than nearly maximally entangled states as this type of resource. This fact brings new insight to the resource theory of state conversion.