Abstract The quantum verification is to determine whether a quantum device is intentionally deceptive by assessing the proximity between the actual output state and the expected state. As a crucial step toward the advancement of quantum technology, numerous quantum state verification methods have been proposed. However, there remains a scarcity of methods for verifying states with an arbitrary number of qubits. A verification strategy for the entangled states with is proposed. Specifically, an average map is introduced and demonstrated that it simplifies the matrix form of the verification strategy while maintaining the verification efficiency. By optimizing the verification strategies, the strategy with local projective measurements is obtained.
Abstract The quantum verification is to determine whether a quantum device is intentionally deceptive by assessing the proximity between the actual output state and the expected state. As a crucial step toward the advancement of quantum technology, numerous quantum state verification methods have been proposed. However, there remains a scarcity of methods for verifying states with an arbitrary number of qubits. A verification strategy for the entangled states with is proposed. Specifically, an average map is introduced and demonstrated that it simplifies the matrix form of the verification strategy while maintaining the verification efficiency. By optimizing the verification strategies, the strategy with local projective measurements is obtained.
Abstract Quantum state verification (QSV) is the task of relying on local measurements only to verify that a given quantum device does produce the desired target state. Up to now, certain types of entangled states can be verified efficiently or even optimally by QSV. However, given an arbitrary entangled state, how to design its verification protocol remains an open problem. This study presents a systematic strategy to tackle this problem by considering the locality of what it initiates as the choice‐independent measurement protocols, whose operators can be directly achieved when they are homogeneous. Taking several typical entangled states as examples, this study shows the explicit procedures of the protocol design using standard Pauli projections, demonstrating the superiority of the method for attaining better QSV strategies. Moreover, the framework can be naturally extended to other tasks such as the construction of entanglement witnesses, and even parameter estimation.
Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterize the output state by quantum state tomography, or alternatively, to perform some kind of Bell test, tailored to the state of interest. We show here that neither approach is optimal among local verification strategies for 2-qubit states. We find the optimal strategy in this case and show that quadratically fewer total measurements are needed to verify to within a given fidelity than in published results for quantum state tomography, Bell test, or fidelity estimation protocols. We also give efficient verification protocols for any stabilizer state. Additionally, we show that requiring that the strategy be constructed from local, nonadaptive, and noncollective measurements only incurs a constant-factor penalty over a strategy without these restrictions.
Abstract The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.
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.
The initialization of a quantum system into a certain state is a crucial aspect of quantum information science. While a variety of measurement strategies have been developed to characterize how well the system is initialized, for a given one, there is in general a trade-off between its efficiency and the accessible information of the quantum state. Conventional quantum state tomography can characterize unknown states while requiring exponentially expensive time-consuming postprocessing. Alternatively, recent theoretical breakthroughs show that quantum state verification provides a technique to quantify the prepared state with significantly fewer samples, especially for multipartite entangled states. In this Letter, we modify the original proposal to be robust to practical imperfections, and experimentally implement a scalable quantum state verification on two-qubit and four-qubit entangled states with nonadaptive local measurements. For all the tested states, the estimated infidelity is inversely proportional to the number of samples, which illustrates the power to characterize a quantum state with a small number of samples. Compared to the globally optimal strategy which requires nonlocal measurements, the efficiency in our experiment is only worse by a small constant factor (<2.5). We compare the performance difference between quantum state verification and quantum state tomography in an experiment to characterize a four-photon Greenberger-Horne-Zeilinger state, and the results indicate the advantage of quantum state verification in both the achieved efficiency and precision.
Abstract Entanglement plays an indispensable role in numerous quantum information and quantum computation tasks, underscoring the need for efficiently verifying entangled states. In recent years, quantum state verification has received increasing attention, yet the challenge of addressing noise effects in implementing this approach remains unsolved. In this work, a systematic assessment of the performance of quantum state verification protocols is provided in the presence of measurement noise. Based on the analysis, a necessary and sufficient condition is provided to uniquely identify the target state under noisy measurements. Moreover, this work proposes a symmetric hypothesis testing verification algorithm with noisy measurements. Then, relying on states, a semidefinite program is demonstrated to calculate the infidelity threshold for arbitrary measurement noise. Subsequently, using a noisy nonadaptive verification strategy of Greenberger–Horne–Zeilinger and stabilizer states, the noise effects on the verification efficiency are analytically illustrated. From both analytical and numerical perspectives, this work demonstrates that the noisy verification protocol exhibits a negative quadratic relationship between the sample complexity and the infidelity. The method can be easily applied to real experimental settings, thereby demonstrating its promising prospects.