Abstract Quantum coherence, as one of the most fundamental non-classical features in quantum mechanics, plays a pivotal role in various quantum information processing tasks, including quantum computing and quantum metrology. The robustness of quantum coherence (RoC) offers an operational interpretation by quantifying the advantage provided by a quantum state in phase discrimination tasks. To achieve verification RoC with high precision via semidefinite programming (SDP), complete knowledge of quantum states is typically required. Relying solely on expectation values of observables may introduce significant errors in SDP-based estimations. To estimate RoC with high precision using limited data extracted from quantum states, firstly, we propose a semi-supervised K-nearest neighbor (KNN) algorithm (semi-KNN) and a semi-supervised method that combines the KNN and random forest (RF) models with a dynamical threshold (semi-KNN-RF). Then we implement the semi-KNN and semi-KNN-RF models to efficiently estimate quantum coherence by analyzing statistical data obtained from randomly generated local projective measurements performed on unknown quantum states. The semi-KNN-RF model performs better than the semi-KNN model. This innovative methodology allows for accurate coherence estimation, even for high-dimensional quantum systems.
Abstract Quantum coherence, as one of the most fundamental non-classical features in quantum mechanics, plays a pivotal role in various quantum information processing tasks, including quantum computing and quantum metrology. The robustness of quantum coherence (RoC) offers an operational interpretation by quantifying the advantage provided by a quantum state in phase discrimination tasks. To achieve verification RoC with high precision via semidefinite programming (SDP), complete knowledge of quantum states is typically required. Relying solely on expectation values of observables may introduce significant errors in SDP-based estimations. To estimate RoC with high precision using limited data extracted from quantum states, firstly, we propose a semi-supervised K-nearest neighbor (KNN) algorithm (semi-KNN) and a semi-supervised method that combines the KNN and random forest (RF) models with a dynamical threshold (semi-KNN-RF). Then we implement the semi-KNN and semi-KNN-RF models to efficiently estimate quantum coherence by analyzing statistical data obtained from randomly generated local projective measurements performed on unknown quantum states. The semi-KNN-RF model performs better than the semi-KNN model. This innovative methodology allows for accurate coherence estimation, even for high-dimensional quantum systems.
Abstract Quantum steering, an intermediate quantum correlation lying between entanglement and nonlocality, has emerged as a critical quantum resource for a variety of quantum information processing tasks such as quantum key distribution and true randomness generation. The ability to detect and quantify quantum steering is crucial for these applications. Semi‐definite programming (SDP) has proven to be a valuable tool to quantify quantum steering. However, the challenge lies in the fact that the optimal measurement strategy is not priori known, making it time‐consuming to compute the steerable measure for any given quantum state. Furthermore, the utilization of SDP requires full information of the quantum state, necessitating quantum state tomography, which can be complex and resource‐consuming. In this work, the semi‐supervised self‐training model is used to estimate the steerable weight, a pivotal measure of quantum steering. The model can be trained using a limited amount of labeled data, thus reducing the time for labeling. The features are constructed by the probabilities derived by performing three sets of projective measurements under arbitrary local unitary transformations on the target states, circumventing the need for quantum tomography. The model demonstrates robust generalization capabilities and can achieve high levels of precision with limited resources.
Abstract Quantum state estimation is a central task in quantum information theory, aiming to reconstruct an unknown density matrix from a finite number of measurement outcomes. Conventional approaches such as kernel smoothing or maximum likelihood estimation (MLE) often rely on restrictive parametric assumptions and become computationally prohibitive for high-dimensional quantum systems. In this work, we introduce a nonparametric quantum state estimation framework based on the k-Nearest Neighbor (k-NN) approach. The method leverages the local geometric structure of measurement data within the quantum feature space to infer the underlying quantum state without any predefined model. Using intrinsic quantum distance metrics—such as the trace distance and quantum fidelity—the proposed estimator identifies neighboring states and performs a weighted aggregation, followed by a positive-semidefinite projection to ensure physical admissibility. We establish the consistency and asymptotic convergence of the NN-based estimator under mild regularity conditions. Numerical simulations on single- and two-qubit systems confirm that the proposed method achieves high reconstruction accuracy, robustness to measurement noise, and superior computational efficiency compared to kernel- and likelihood-based estimators. Overall, this study highlights the potential of data-driven, geometry-aware, nonparametric learning for scalable quantum state reconstruction, providing a promising alternative for modern quantum information processing.
Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. Here, the robustness of coherence is defined and proven to be a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is finally provided: the robustness of coherence quantifies the advantage enabled by a quantum state in a phase discrimination task.
Quantum coherence is a crucial resource in numerous quantum processing tasks. The robustness of coherence provides an operational measure of quantum coherence, which can be calculated for various states using semidefinite programming. However, this method depends on convex optimization and can be time-intensive, especially as the dimensionality of the space increases. In this study, we employ machine learning techniques to quantify quantum coherence, focusing on the robustness of coherence. By leveraging artificial neural networks, we developed and trained models for systems with different dimensionalities. Testing on data samples shows that our approach substantially reduces computation time while maintaining strong generalizability.
Quantum coherence has wide-ranging applications from quantum thermodynamics to quantum metrology, quantum channel discrimination, and even quantum biology. Thus, detecting and quantifying coherence are two fundamental problems in quantum resource theory. Here, we introduce feasible methods to detect and estimate the coherence by constructing coherence witnesses for any finite-dimensional states. Our coherence witnesses detect coherent states by testing whether the expectation value of the witness is negative or not. Two typical coherence witnesses are proposed and discussed based on our witness-constructing method, which are also used to estimate the robustness of coherence, the l1 norm, and the l2 norm of coherence measures. Furthermore, we compare one of our coherence witnesses with a previously introduced witness by proving that our witness is strictly stronger than that previous witness. We also present an application of coherence in a quantum metrology task, in which we estimate an unknown parameter by measuring our coherence witness.
ABSTRACT A quantum K‐nearest neighbors(QKNN) algorithm is proposed to offer superior performance compared to the classical KNN(CKNN) approach, improving classification accuracy, scalability, and robustness. Our approach optimizes Hadamard and rotation gates for quantum data encoding and efficiently embeds classical data into quantum states. Entangled gates, such as IsingXY and CNOT, enhance feature extraction and classification by enabling complex feature interactions. A new quantum distance metric based on swap test results is used to calculate similarity measures between quantum states. This algorithm offers superior accuracy and computational efficiency compared to traditional Euclidean distance metrics. We used three benchmark datasets to evaluate the suggested QKNN method. The results demonstrated that it outperformed the other two methods, classical KNN (CKNN) and quantum neural networks (QNN), as well as the more recent QKNN research. The proposed QKNN algorithm achieves prediction accuracies of 98.25%, 100%, and 99.27% for the three datasets, whereas the QNN achieves prediction accuracies of 97.17%, 83.33%, and 86.18%, respectively. Moreover, quantum noise challenges are addressed by integrating a Shor code‐based error mitigation strategy, which ensures stability of the algorithm and resilience to noisy quantum environments. The results demonstrate the scalability, efficiency, and robustness of the proposed QKNN algorithm.