Computable entanglement conversion witness that is better than the negativity

TL;DR

This paper introduces a new, efficiently computable entanglement conversion witness that outperforms negativity and sometimes surpasses entanglement of formation in detecting state interconvertibility.

Contribution

The authors develop a novel conversion witness that is computationally efficient and more effective than existing measures like negativity, with potential applications beyond entanglement.

Findings

The conversion witness outperforms negativity in detecting non-interconvertibility.

It is sometimes better than entanglement of formation for two-qubit states.

The witness is efficiently computable for arbitrary states and system sizes.

Abstract

The primary goal of entanglement theory is to determine convertibility conditions for two quantum states. Up until now, this has always been done with the use of entanglement monotones. With the exception of the negativity, such quantities tend to be rather uncomputable. We instead promote the idea of conversion witnesses in this paper. A conversion witness is a function on pairs of states and whose value determines whether a state can be converted into another. We construct a conversion witness that can be efficiently computed for arbitrary states in systems of any size. This conversion witness is always better than the negativity at detecting when two entangled states are not interconvertible. Furthermore, when considering states of two-qubit systems, this new conversion witness is sometimes better than the entanglement of formation. This shows that the study of conversion witness is in fact useful, and may have applications in resource theories beyond that of entanglement.