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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.
Concomitant with the rapid development of quantum technologies, challenging demands arise concerning the certification and characterization of devices. The promises of the field can only be achieved if stringent levels of precision of components can
Standard Bayesian credible-region theory for constructing an error region on the unique estimator of an unknown state in general quantum-state tomography to calculate its size and credibility relies on heavy Monte~Carlo sampling of the state space fo
Recently [Cavalcanti textit{et al.} Nat Commun textbf{6}, 7941 (2015)] proposed a method to certify the presence of entanglement in asymmetric networks, where some users do not have control over the measurements they are performing. Such asymmetry na
We study the quantum query complexity of finding a certificate for a d-regular, k-level balanced NAND formula. Up to logarithmic factors, we show that the query complexity is Theta(d^{(k+1)/2}) for 0-certificates, and Theta(d^{k/2}) for 1-certificate
We investigate the optimal quantum state reconstruction from cloud to many spatially separated users by measure-broadcast-prepare scheme without the availability of quantum channel. The quantum state equally distributed from cloud to arbitrary number