Among various multipartite entangled states, Dicke states stand out because their entanglement is maximally persistent and robust under particle losses. Although they have attracted much attention for their potential applications in quantum information processing and foundational studies, the characterization of Dicke states remains as a challenging task in experiments. Here we propose efficient and practical protocols for verifying arbitrary $n$-qubit Dicke states in both adaptive and nonadaptive ways. Our protocols require only two distinct settings based on Pauli measurements besides permutations of the qubits. To achieve infidelity $ϵ$ and confidence level $1-\delta$, the total number of tests required is only $O(n{ϵ}^{-1}\ln {\delta }^{-1})$. This performance is exponentially more efficient than all previous protocols based on local measurements, including quantum state tomography and direct fidelity estimation, and is comparable to the best global strategy. Our protocols are readily applicable with current experimental techniques and are able to verify Dicke states of hundreds of qubits.

Quantum processes, such as quantum circuits, quantum memories, and quantum channels, are essential ingredients in almost all quantum information processing tasks. However, the characterization of these processes remains a daunting task due to the exponentially increasing amount of resources required by traditional methods. Here, by first proposing the concept of quantum process verification, we establish two efficient and practical protocols for verifying quantum processes which can provide an exponential improvement over the standard quantum process tomography and a quadratic improvement over the method of direct fidelity estimation. The efficacy of our protocols is illustrated with the verification of various quantum gates as well as the processes of well-known quantum circuits. Moreover, our protocols are readily applicable with current experimental techniques since only local measurements are required. In addition, we show that our protocols for verifying quantum processes can be easily adapted to verify quantum measurements.

The efficient and reliable characterization of quantum states plays a vital role in most, if not all, quantum information processing tasks. In this work, we present a universally optimal protocol for verifying entangled states by employing the so-called quantum nondemolition measurements, such that the verification efficiency is equivalent to that of the optimal global strategy. Instead of being probabilistic as the standard verification strategies, our protocol is constructed sequentially, which is thus more favorable for experimental realizations. In addition, the target states are preserved in the protocol after each measurement, so can be reused in any subsequent tasks. We demonstrate the power of our protocol for the optimal verification of Bell states, arbitrary two-qubit pure states, and stabilizer states. We also prove that our protocol is able to perform tasks including fidelity estimation and state preparation.

Continuous-variable quantum states are of particular importance in various quantum information processing tasks including quantum communication and quantum sensing. However, a bottleneck has emerged with the fast increasing in size of the quantum systems which severely hinders their efficient characterization. In this work, we establish a systematic framework for verifying entangled continuous-variable quantum states by employing local measurements only. Our protocol is able to achieve the unconditionally high verification efficiency which is quadratically better than quantum tomography as well as other nontomographic methods. Specifically, we demonstrate the power of our protocol by showing the efficient verification of entangled two-mode and multimode coherent states with local measurements.