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

We address the problem of constructing positive operator-valued measures(POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one whichhave an inner product close to uniform. This is motivated by the relatedquestion of constructing symmetric informationally complete POVMs (SIC-POVMs)for which the inner products are perfectly uniform. However, SIC-POVMs arenotoriously hard to construct and despite some success of constructing themnumerically, there is no analytic construction known. We present twoconstructions of approximate versions of SIC-POVMs, where a small deviationfrom uniformity of the inner products is allowed. The first construction isbased on selecting vectors from a maximal collection of mutually unbiased basesand works whenever the dimension of the system is a prime power. The secondconstruction is based on perturbing the matrix elements of a subset of mutuallyunbiased bases.  Moreover, we construct vector systems in $\C^n$ which are almost orthogonaland which might turn out to be useful for quantum computation. Ourconstructions are based on results of analytic number theory.Comment: 29 pages, LaTe

On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states