Abstract Entanglement detection, the process of verifying quantum entanglement is a fundamental challenge in quantum information processing. Various approaches have been proposed to address this challenge, with many recent studies applying supervised machine learning methods. While these methods have demonstrated high accuracy in entanglement detection, it is reasonable to assume that the entangled states themselves are not definitively known. To address this limitation, we have devised a machine learning method for entanglement detection based on positive-unlabeled learning, a classical machine learning framework that does not use label information from negative data. Using a deep neural network model to synthetic dataset under the assumption of mixed states, we conducted experiments on a classical computer to valid the effectiveness and characteristics of the proposed method. Our approach introduces a novel framework that accounts for the data generation constraints in the training process of entanglement detector, thereby advancing machine learning techniques in quantum information science.

Abstract This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus on bipartite systems of dimensions $$3\times 3$$ 3 × 3 , $$4\times 4$$ 4 × 4 , and $$5\times 5$$ 5 × 5 , where the positive partial transpose criterion (PPT) provides only partial characterization. Using SVMs with quantum-inspired kernels, we develop a classification scheme that distinguishes between separable and entangled states, including PPT-detectable entangled states, and entangled states that evade PPT detection. Our method achieves increasing accuracy with system dimension, reaching $$80\%$$ 80 % , $$90\%$$ 90 % , and nearly $$100\%$$ 100 % for $$3\times 3$$ 3 × 3 , $$4\times 4$$ 4 × 4 , and $$5\times 5$$ 5 × 5 systems, respectively. Our results show that principal component analysis significantly enhances performance for small training sets. The study reveals important practical considerations regarding purity biases in the generation of data for this problem and examines the challenges of implementing these techniques on near-term quantum hardware. Our results demonstrate that machine learning can be an effective alternative to entanglement detection of higher-dimensional systems where conventional entanglement detection methods struggle. Our approach provides improved data generation protocols and can be readily implemented in hybrid classical-quantum architectures, overcoming current limitations.

Entanglement detection beyond the local bound with coarsely calibrated measurements

ABSTRACT The experimental detection of quantum entanglement is of great importance in quantum information processing. We present two separability criteria based on the generalized realignment moments. By incorporating additional parameters, these criteria prove to be more flexible and stronger than some of the existing ones. Detailed examples are given to demonstrate their availability and feasibility for entanglement detection.

Rank-based entanglement detection for bound entangled states

Abstract We compute all third-order local invariants accessible via randomized measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite states with arbitrary local dimensions. The results show that third-order invariants capture inter-subsystem correlations beyond second-order spectral criteria within more feasible entanglement detection protocols than full tomography. As an example, for Werner states in d = 3, the entanglement is detected for p > 1 2 for the second-order correlations and it is improved to p > 1 10 3 at the third-order.

Abstract This paper presents an optical scheme for realizing the Hadamard gate (HG) using linear optical elements, including a beam splitter (BS) and a phase shifter, and explores its application in a novel interferometer design. Key aspects investigated include phase sensitivity via quantum Fisher information (QFI) and intensity-based detection methods, entanglement detection using the Shchukin-Vogel (SV) criteria, polarization properties through Stokes operators, and quantum squeezing effects, including difference and sum squeezing. Results indicate that the interferometer achieves phase sensitivity below the shot-noise limit (SNL), approaching the Heisenberg limit (HL) in specific regimes, and exhibits strong non-classical behaviors such as entanglement and squeezing, particularly at low photon numbers and specific phase angles. This work highlights the potential of HG-based interferometers for advanced quantum information processing and precision measurement applications.

High-speed generation and efficient entanglement detection on a photonic chip are essential for quantum information applications but hard to achieve due to common photonic chips’ material properties and limited component performance. In this work, we experimentally demonstrate an entanglement witness on a silicon photonic chip, with multi-rail single-photon entanglement generation based on decoy-state techniques. The detection is based on balanced homodyne detectors on the same photonic chip with a bandwidth of up to 12.5 GHz, which allows room-temperature operation. A loss-equivalent analysis method compensates for optical losses and system noises. Experimental results quantify an entangled state fidelity of 92% in quantum state tomography and a Clauser–Horne–Shimony–Holt violation lower bound of 2.59. These results establish a viable path toward fully integrated, high-bandwidth, room-temperature quantum photonic systems, with potential applications in on-chip quantum optics and quantum random number generation.

The reliable detection of entanglement plays a crucial role in the construction of quantum networks. The conventional entanglement witness (EW) method has high requirements for measurement device and relies on reliable implementation of the measurement. With unreliable measurement device, EW process can be easily attacked by eavesdroppers, which can lead to incorrect entanglement detection results. Therefore, a feasible and secure measurement device independent entanglement witness (MDIEW) method is desired for constructing quantum networks. Here, we detect the continuous variable entanglement by a MDIEW in a quantum network. It is demonstrated that the conventional EW method can be affected when the local oscillator intensity is changed, while the MDIEW method can detect entanglement between users without being affected. Our results provide a trustworthy method to detect entanglement, which is an important step for constructing secure quantum networks.

Multipartite Einstein–Podolsky–Rosen (EPR) steering plays a crucial role in realizing secure quantum communication. In this paper, we theoretically investigate bipartite and tripartite quantum correlations, including entanglement and Gaussian quantum steering, in a cavity magnomechanical system incorporating a coherent feedback loop. We quantify and compare entanglement and Gaussian steering for four coupled bipartite Gaussian modes. Our results show that tuning the beam splitter’s reflectivity parameter significantly enhances entanglement in both bipartite and tripartite states. Furthermore, we verify Coffman–Kundu–Wootters (CKW)-type monogamy inequalities for Gaussian steering among three tripartite modes for specific reflectivity values, and reveal the presence of one-way steering. These findings validate our system and demonstrate its potential for robust detection of multipartite entanglement and steering.

The efficient error correction subsystem is essential for quantum computing and communication systems due to challenges like no-cloning and destructive measurements. Error-correction codes and fault-tolerant technologies are vital for mitigating errors. Our focus is on implementing fault-tolerant encoding circuits based on Steane code within optical integrated circuits using two C-NOT structures that utilize nonlinear optics. A Mach-Zehnder structure made from Si3N4 and nonlinear material with a nonlinear coefficient of n2 = - 3.5 × 10-15m2/W (the nanocrystal of PbS), is exposed to 1.55μm wavelength waves, where propagated modes serve as qubits. The main input state delivers 25μW per 100nm2, and secondary inputs provide 15μW per 100nm2, allowing entanglement and error detection among qubits. The design has achieved a fidelity of F > 0.89, crucial for effective error correction in photon-based quantum computations.

Abstract Recently, machine learning has been widely applied in the field of quantum information, notably in tasks such as entanglement detection, steering characterization, and nonlocality verification. However, few studies have focused on utilizing machine learning to detect quantum information masking (QIM). In this work, we investigate supervised machine learning for detecting QIM in both pure and mixed qubit states. For pure qubit states, we randomly generate the corresponding density matrices and train an XGBoost model to detect QIM. For mixed qubit states, we improve the XGBoost method by optimizing the selection of training samples. The experimental results demonstrate that our approach achieves higher classification accuracy. Furthermore, we analyze the area under the curve of the receiver operating characteristic curve for this method, which further confirms its classification performance.

As quantum computing advances, traditional digital forensic techniques face significant risks due to the vulnerability of classical cryptographic algorithms to quantum attacks. This review explores the emerging field of quantum digital forensics, with a particular focus on the role of quantum entanglement in enhancing the integrity, authenticity, and confidentiality of digital evidence. It compares classical and quantum forensic mechanisms, examines entanglement-based quantum key distribution (QKD), quantum hash functions, and quantum digital signatures (QDS), and discusses the challenges in practical implementation, such as scalability, hardware limitations, and legal admissibility. The paper also reviews various entanglement detection methods critical to the validation of quantum states used in forensic processes.

Multipartite entanglement is an essential resource for quantum information tasks, but characterizing entanglement structures in continuous-variable systems remains challenging, especially in multimode non-Gaussian scenarios. In this Letter, we introduce an efficient method for detecting multipartite entanglement structures in continuous-variable states. Based on the quantum Fisher information, we propose a systematic approach to identify an encoding operator that can efficiently capture the quantum correlations in multimode non-Gaussian states. We demonstrate the effectiveness of our method on over 10^{5} randomly generated multimode-entangled quantum states, achieving a very high success rate in entanglement detection. Additionally, the robustness of our method can be considerably enhanced against losses by expanding the set of accessible operators. This Letter provides a general framework for characterizing entanglement structures in diverse continuous-variable systems, enabling a number of experimentally relevant applications.

Entanglement is the cornerstone of quantum communication, yet conventional detection relies solely on local measurements. In this Letter, we present an experimental demonstration, based on an improved theoretical framework showing that one-way local operations and classical communication (1-LOCC) can significantly outperform purely local measurements in detecting quantum entanglement. By casting the entanglement detection problem as a semidefinite program, we derive protocols that minimize false negatives at fixed false-positive rates. A variational generative machine-learning algorithm efficiently searches over high-dimensional parameter spaces, identifying states and measurement strategies that exhibit a clear 1-LOCC advantage. Experimentally, we realize a genuine event-ready protocol on a three-dimensional photonic entanglement source, employing fiber delays as short-lived quantum memories. We implement rapid, field-programmable gate array-based sampling of the optimized probabilistic instructions, allowing Bob's measurement settings to adapt to Alice's outcomes in real time. Our results validate the predicted 1-LOCC advantage in a realistic noisy setting and reduce the experimental trials needed to certify entanglement. These findings mark a step toward scalable, adaptive entanglement detection methods crucial for quantum networks and computing, paving the way for more efficient generation and verification of high-dimensional entangled states.

Entanglement has the ability to enhance the transmission of classical information over a quantum channel. However, fully harvesting this advantage typically requires complex entangling measurements, which are challenging to implement and scale with the system's size. In this Letter, we consider a natural quantum information primitive known as a random access code in which the message to be communicated is selected stochastically. We introduce a protocol that leverages high-dimensional entanglement to perform this task perfectly, without requiring quantum interference between particles at the measurement station. We experimentally demonstrate how this unlocks implementation in the high-dimensional regime through an optical setup using eight-dimensional entanglement and multioutcome detection, providing a practical solution for stochastic communication and a robust method for certifying the dimensionality of entanglement in communication experiments.

Abstract Quantum measurements are important tools in quantum information, represented by positive, operator-valued measures. A wide class of symmetric measurements is given via generalized equiangular measurements (GEAMs) that form conical 2-designs. We show that only two positive constants are needed to fully characterize a variety of important quantum measures constructed from such operators. Examples are given for entropic uncertainty relations, the Brukner–Zeilinger invariants, quantum coherence, quantum concurrence, and the Schmidt-number criterion for entanglement detection. Our results indicate that similar relations may also hold for conical 2-designs from beyond the class of GEAMs.

The efficient witnessing and certification of entanglement is necessitated by its ubiquitous use in various aspects of quantum technologies. In the case of continuous-variable bipartite systems, the Shchukin-Vogel hierarchy gives necessary conditions for separability in terms of moments of the mode operators. In this work we derive mode-operator-based witnesses for continuous-variable bipartite entanglement relying on the interference of two states. Specifically, we show how one can access higher moments of the mode operators, crucial for detecting entanglement of non-Gaussian states, using a single beamsplitter with variable phase and photon-number-resolving detectors. We demonstrate that the use of an entangled state paired with a suitable reference state is sufficient to detect entanglement in, e.g., two-mode squeezed vacuum, NOON states, and mixed entangled cat states. We also take into account experimental noise, including photon loss and detection inefficiency, as well as finite measurement statistics.

Estimating the trace of quantum state powers, Tr(ρk), for k identical quantum states is a fundamental task with numerous applications in quantum information processing, including nonlinear function estimation of quantum states and entanglement detection. On near-term quantum devices, reducing the required quantum circuit depth, the number of multi-qubit quantum operations, and the copies of the quantum state needed for such computations is crucial. In this work, inspired by the Newton-Girard method, we significantly improve upon existing results by introducing an algorithm that requires only O(r~) qubits and O(r~) multi-qubit gates, where r~=min{rank(ρ),⌈ln⁡(2k/ϵ)⌉}. This approach is efficient, as it employs the r~-entangled copy measurement instead of the conventional k-entangled copy measurement, while asymptotically preserving the known sample complexity upper bound. Furthermore, we prove that estimating {Tr(ρi)}i=1r~ is sufficient to approximate Tr(ρk) even for large integers k>r~. This leads to a rank-dependent complexity for solving the problem, providing an efficient algorithm for low-rank quantum states while also improving existing methods when the rank is unknown or when the state is not low-rank. Building upon these advantages, we extend our algorithm to the estimation of Tr(Mρk) for arbitrary observables and Tr(ρkσl) for multiple quantum states.

Abstract In the noisy intermediate‐scale quantum (NISQ) era, multipartite entanglement in realistic noisy environments exhibits complex structures. Characterizing entanglement structures—particularly entanglement depth and intactness—has become increasingly essential for quantum information processing tasks. Traditional methods like standard entanglement witnesses assume that experimenters can exactly implement specific quantum measurements. Even minor inaccuracies in standard witness can introduce significant errors in entanglement detection. Certification methods are proposed with relaxed assumptions about the system and measurements for entanglement structures. First, entanglement states are classified with the same intactness into three distinct types based on their depth. Next, analytical witnesses are derived to detect the entanglement structure of general n‐qubit systems in both device‐independent and semi‐device‐independent scenarios, where some observables are untrusted while others remain reliable. Furthermore, this framework is extended to account for small measurement imperfections, ensuring robustness in practical settings. It is demonstrated that this witness can detect larger entanglement regions compared to previous Bell‐type inequalities. Remarkably, for Type I 4‐partite quantum states, this entanglement witness with measurement imperfections is identical to both device‐dependent and semi‐device‐independent approaches.