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 study efficient quantum certification algorithms for quantum state set andunitary quantum channel. We present an algorithm that uses$O(\varepsilon^{-4}\ln |\mathcal{P}|)$ copies of an unknown state todistinguish whether the unknown state is contained in or $\varepsilon$-far froma finite set $\mathcal{P}$ of known states with respect to the trace distance.This algorithm is more sample-efficient in some settings. Previous study showedthat one can distinguish whether an unknown unitary $U$ is equal to or$\varepsilon$-far from a known or unknown unitary $V$ in fixed dimension with$O(\varepsilon^{-2})$ uses of the unitary, in which the Choi state is used andthus an ancilla system is needed. We give an algorithm that distinguishes thetwo cases with $O(\varepsilon^{-1})$ uses of the unitary, using much fewer orno ancilla compared with previous results.

Quantum certification of state set and unitary channel