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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Tensor rank refers to the number of product states needed to express a givenmultipartite quantum state. Its non-additivity as an entanglement measure hasrecently been observed. In this note, we estimate the tensor rank of multiplecopies of the tripartite state$\ket{W}=\tfrac{1}{\sqrt{3}}(\ket{100}+\ket{010}+\ket{001})$. Both an upperbound and a lower bound of this rank are derived. In particular, it is proventhat the tensor rank of $\ket{W}^{\otimes 2}$ is seven, thus resolving apreviously open problem. Some implications of this result are discussed interms of transformation rates between $\ket{W}^{\otimes n}$ and multiple copiesof the state $\ket{GHZ}=\tfrac{1}{\sqrt{2}}(\ket{000}+\ket{111})$.

The Tensor Rank of the Tripartite State $\ket{W}^{\otimes n}$}