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

We provide two sufficient and necessary conditions to characterize any$n$-bit partial Boolean function with exact quantum 1-query complexity. Usingthe first characterization, we present all $n$-bit partial Boolean functionsthat depend on $n$ bits and have exact quantum 1-query complexity. Due to thesecond characterization, we construct a function $F$ that maps any $n$-bitpartial Boolean function to some integer, and if an $n$-bit partial Booleanfunction $f$ depends on $k$ bits and has exact quantum 1-query complexity, then$F(f)$ is non-positive. In addition, we show that the number of all $n$-bitpartial Boolean functions that depend on $k$ bits and have exact quantum1-query complexity is not bigger than $n^{2}2^{2^{n-1}(1+2^{2-k})+2n^{2}}$ forall $n\geq 3$ and $k\geq 2$.

Partial Boolean functions with exact quantum 1-query complexity