English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article we provide a three step algorithm to obtain the ClosestSeparable State to the given state in Hilbert space dimensions $2\times 2$ and$2\times 3$, or in the higher dimensional Hilbert spaces, 'Closest PositivePartial Transpose (PPT) state' for the chosen bipartition. In the process, atight lower bound to the minimum Hilbert-Schmidt distance is brought forthtogether with the relation between the minimum Hilbert-Schmidt distance andNegativity. This also leads us to discuss the validity of the said distancefrom the set of separable quantum states as an entanglement measure. AnyEntanglement measure defined as the minimum of a distance measure to the set ofseparable states needs to follow certain widely accepted rules. Mostsignificantly, contractiveness of the distance (also, CP non-expansiveproperty) under LOCC maps. While the Hilbert-Schmidt distance does not havethis property, it is still an open question if the measure constructed using itis non-increasing under LOCC operations. While we outline some of thedifficulties in such a proof, we also provide numerical evidence that bringsone step closer to closing the question.

Minimum Hilbert-Schmidt distance and the Closest Separable state to arbitrary $2 \times 2$ and $2 \times 3$ states