Quantum certification of state set and unitary channel

TL;DR

This paper introduces more efficient quantum certification algorithms for identifying whether an unknown quantum state belongs to a known set or whether an unknown unitary operation matches a known or unknown unitary, reducing resource requirements.

Contribution

It presents novel algorithms that improve sample and resource efficiency for quantum state and unitary channel certification compared to prior methods.

Findings

Sample complexity for state certification is reduced to $O(\u03b5^{-4}\, ext{ln}|\u2115|)$

Unitary channel distinction requires only $O(\u03b5^{-1})$ uses, fewer than previous methods

Algorithms use fewer or no ancilla systems, simplifying implementation

Abstract

We study efficient quantum certification algorithms for quantum state set and unitary quantum channel. We present an algorithm that uses $O(\varepsilon^{-4}\ln |\mathcal{P}|)$ copies of an unknown state to distinguish whether the unknown state is contained in or $\varepsilon$-far from a finite set $\mathcal{P}$ of known states with respect to the trace distance. This algorithm is more sample-efficient in some settings. Previous study showed that 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 and thus an ancilla system is needed. We give an algorithm that distinguishes the two cases with $O(\varepsilon^{-1})$ uses of the unitary, using much fewer or no ancilla compared with previous results.