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Quantum state verification provides an efficient approach to characterize the reliability of quantum devices for generating certain target states. The figure of merit of a specific strategy is the estimated infidelity $epsilon$ of the tested state to the target state, given a certain number of performed measurements n. Entangled measurements constitute the globally optimal strategy and achieve the scaling that epsilon is inversely proportional to n. Recent advances show that it is possible to achieve the same scaling simply with non-adaptive local measurements, however, the performance is still worse than the globally optimal bound up to a constant factor. In this work, by introducing classical communication, we experimentally implement an adaptive quantum state verification. The constant-factor is minimized from ~2.5 to 1.5 in this experiment, which means that only 60% measurements are required to achieve a certain value of epsilon compared to optimal non-adaptive local strategy. Our results indicate that classical communication significantly enhances the performance of quantum state verification, and leads to an efficiency that further approaches the globally optimal bound.
We present and experimentally demonstrate a communication protocol that employs shared entanglement to reduce errors when sending a bit over a particular noisy classical channel. Specifically, it is shown that, given a single use of this channel, one
We present a classical interactive protocol that verifies the validity of a quantum witness state for the local Hamiltonian problem. It follows from this protocol that approximating the non-local value of a multi-player one-round game to inverse poly
We present an experiment demonstrating entanglement-enhanced classical communication capacity of a quantum channel with correlated noise. The channel is modelled by a fiber optic link exhibiting random birefringence that fluctuates on a time scale mu
We study the capacity of d-dimensional quantum channels with memory modeled by correlated noise. We show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher valu
In this paper, we extend the protocol of classical verification of quantum computations (CVQC) recently proposed by Mahadev to make the verification efficient. Our result is obtained in the following three steps: $bullet$ We show that parallel repe