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

Quantifying coherence and entanglement is extremely important in quantuminformation processing. Here, we present numerical and analytical results forthe geometric measure of coherence, and also present numerical results for thegeometric measure of entanglement. On the one hand, we first provide asemidefinite algorithm to numerically calculate geometric measure of coherencefor arbitrary finite-dimensional mixed states. Based on this semidefinitealgorithm, we test randomly generated single-qubit states, single-qutritstates, and a special kind of $d$-dimensional mixed states. Moreover, we alsoobtain an analytical solution of geometric measure of coherence for a specialkind of mixed states. On the other hand, another algorithm is proposed tocalculate the geometric measure of entanglement for arbitrary two-qubit andqubit-qutrit states, and some special kinds of higher dimensional mixed states.For other states, the algorithm can get a lower bound of the geometric measureof entanglement. Randomly generated two-qubit states, the isotropic states andthe Werner states are tested. Furthermore, we compare our numerical resultswith some analytical results, which coincide with each other.

Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement