Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose an operational scheme to measure the entanglement --- as given by the negativity --- between arbitrary subsystems of size $N_A$ and $N_B$ , with $\mathcal{O}(N_A + N_B)$ measurements, and without any prior knowledge of the state. We propose how to experimentally measure the partially transposed moments of a density matrix, and using just the first few of these, extract the negativity via Chebyshev approximation or machine learning techniques. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many body systems in both equilibrium and non-equilibrium regimes.Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose an operational scheme to measure the entanglement --- as given by the negativity --- between arbitrary subsystems of size $N_A$ and $N_B$, with $\mathcal{O}(N_A + N_B)$ measurements, and without any prior knowledge of the state. We propose how to experimentally measure the partially transposed moments of a density matrix, and using just the first few of these, extract the negativity via Chebyshev approximation or machine learning techniques. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many body systems in both equilibrium and non-equilibrium regimes.

Sep 14, 20175 citations

Measuring Quantum Entanglement from Local Information by Machine Learning

Yulei Huang, Liangyu Che, Wei, Chao +5 more

Entanglement is a key property in the development of quantum technologies and in the study of quantum many-body simulations. However, entanglement measurement typically requires quantum full-state tomography (FST). Here we present a neural network-assisted protocol for measuring entanglement in equilibrium and non-equilibrium states of local Hamiltonians. Instead of FST, it can learn comprehensive entanglement quantities from single-qubit or two-qubit Pauli measurements, such as Rényi entropy, partially-transposed (PT) moments, and coherence. It is also exciting that our neural network is able to learn the future entanglement dynamics using only single-qubit traces from the previous time. In addition, we perform experiments using a nuclear spin quantum processor and train an adoptive neural network to study entanglement in the ground and dynamical states of a one-dimensional spin chain. Quantum phase transitions (QPT) are revealed by measuring static entanglement in ground states, and the entanglement dynamics beyond measurement time is accurately estimated in dynamical states. These precise results validate our neural network. Our work will have a wide range of applications in quantum many-body systems, from quantum phase transitions to intriguing non-equilibrium phenomena such as quantum thermalization.Entanglement is a key property in the development of quantum technologies and in the study of quantum many-body simulations. However, entanglement measurement typically requires quantum full-state tomography (FST). Here we present a neural network-assisted protocol for measuring entanglement in equilibrium and non-equilibrium states of local Hamiltonians. Instead of FST, it can learn comprehensive entanglement quantities from single-qubit or two-qubit Pauli measurements, such as Rényi entropy, partially-transposed (PT) moments, and coherence. It is also exciting that our neural network is able to learn the future entanglement dynamics using only single-qubit traces from the previous time. In addition, we perform experiments using a nuclear spin quantum processor and train an adoptive neural network to study entanglement in the ground and dynamical states of a one-dimensional spin chain. Quantum phase transitions (QPT) are revealed by measuring static entanglement in ground states, and the entanglement dynamics beyond measurement time is accurately estimated in dynamical states. These precise results validate our neural network. Our work will have a wide range of applications in quantum many-body systems, from quantum phase transitions to intriguing non-equilibrium phenomena such as quantum thermalization.

arXiv:2209.08501Sep 18, 20221 citation

Quantifying Unknown Multiqubit Entanglement Using Machine Learning

Yukun Wang, Shaoxuan Wang, Jincheng Xing +2 more

Entanglement plays a pivotal role in numerous quantum applications, and as technology progresses, entanglement systems continue to expand. However, quantifying entanglement is a complex problem, particularly for multipartite quantum states. The currently available entanglement measures suffer from high computational complexity, and for unknown multipartite entangled states, complete information about the quantum state is often necessary, further complicating calculations. In this paper, we train neural networks to quantify unknown multipartite entanglement using input features based on squared entanglement (SE) and outcome statistics data produced by locally measuring target quantum states. By leveraging machine learning techniques to handle non-linear relations between outcome statistics and entanglement measurement SE, we achieve high-precision quantification of unknown multipartite entanglement states with a linear number of measurements, avoiding the need for global measurements and quantum state tomography. The proposed method exhibits robustness against noise and extends its applicability to pure and mixed states, effectively scaling to large-scale multipartite entanglement systems. The results of the experiment show that the predicted entanglement measures are very close to the actual values, which confirms the effectiveness of the proposed method.Entanglement plays a pivotal role in numerous quantum applications, and as technology progresses, entanglement systems continue to expand. However, quantifying entanglement is a complex problem, particularly for multipartite quantum states. The currently available entanglement measures suffer from high computational complexity, and for unknown multipartite entangled states, complete information about the quantum state is often necessary, further complicating calculations. In this paper, we train neural networks to quantify unknown multipartite entanglement using input features based on squared entanglement (SE) and outcome statistics data produced by locally measuring target quantum states. By leveraging machine learning techniques to handle non-linear relations between outcome statistics and entanglement measurement SE, we achieve high-precision quantification of unknown multipartite entanglement states with a linear number of measurements, avoiding the need for global measurements and quantum state tomography. The proposed method exhibits robustness against noise and extends its applicability to pure and mixed states, effectively scaling to large-scale multipartite entanglement systems. The results of the experiment show that the predicted entanglement measures are very close to the actual values, which confirms the effectiveness of the proposed method.

EntropyFeb 12, 20253 citations

Entanglement quantification via weak measurements assisted by deep learning

Mu Yang, Xiao Ya, Ze-Yan Hao +9 more

Entanglement has been recognized as being crucial when implementing various quantum information tasks. Nevertheless, quantifying entanglement for an unknown quantum state requires nonphysical operations or post-processing measurement data. For example, evaluation methods via quantum state tomography require vast amounts of measurement data and likely estimation. Although a direct entanglement determination has been reported for the unknown pure state, it is still tricky for the mixed state. In this work, assisted by weak measurement and deep learning technology, we directly detect the entanglement (namely, the concurrence) of a class of two-photon polarization-entangled mixed states both theoretically and experimentally according to the local photon spatial distributions after weak measurement. In this way, the number of projective bases is much smaller than that required in quantum state tomography.Entanglement has been recognized as being crucial when implementing various quantum information tasks. Nevertheless, quantifying entanglement for an unknown quantum state requires nonphysical operations or post-processing measurement data. For example, evaluation methods via quantum state tomography require vast amounts of measurement data and likely estimation. Although a direct entanglement determination has been reported for the unknown pure state, it is still tricky for the mixed state. In this work, assisted by weak measurement and deep learning technology, we directly detect the entanglement (namely, the concurrence) of a class of two-photon polarization-entangled mixed states both theoretically and experimentally according to the local photon spatial distributions after weak measurement. In this way, the number of projective bases is much smaller than that required in quantum state tomography.

Photonics ResearchDec 11, 20234 citations

Direct entanglement detection of quantum systems using machine learning

Yulei Huang, Liangyu Che, Chao Wei +5 more

Entanglement plays a crucial role in advancing quantum technologies and exploring quantum many-body simulations. Here, we introduce a protocol aided by neural networks for measuring entanglement in both equilibrium and non-equilibrium states of local Hamiltonians, with a favorable amount of training data. Our numerical simulations across various Hamiltonian models and qubit configurations reveal that this approach can predict comprehensive entanglement metrics, such as Rényi entropy, for up to 100 qubits using only single-qubit and two-qubit Pauli measurements. Excitingly, future entanglement dynamics beyond the measurement window can be predicted based solely on previous single-qubit traces. Experimentally, we utilize a nuclear spin quantum processor and a neural network to measure entanglement in the ground and dynamical states of a one-dimensional spin chain. The results demonstrate the feasibility of our method in practical experiments. Therefore, our approach offers a promising method for experimentally measuring entanglement in systems with dozens to hundreds of qubits.Entanglement plays a crucial role in advancing quantum technologies and exploring quantum many-body simulations. Here, we introduce a protocol aided by neural networks for measuring entanglement in both equilibrium and non-equilibrium states of local Hamiltonians, with a favorable amount of training data. Our numerical simulations across various Hamiltonian models and qubit configurations reveal that this approach can predict comprehensive entanglement metrics, such as Rényi entropy, for up to 100 qubits using only single-qubit and two-qubit Pauli measurements. Excitingly, future entanglement dynamics beyond the measurement window can be predicted based solely on previous single-qubit traces. Experimentally, we utilize a nuclear spin quantum processor and a neural network to measure entanglement in the ground and dynamical states of a one-dimensional spin chain. The results demonstrate the feasibility of our method in practical experiments. Therefore, our approach offers a promising method for experimentally measuring entanglement in systems with dozens to hundreds of qubits.

npj Quantum InformationFeb 20, 202518 citations

Self-Attention for Quantum Entanglement Prediction

Anuj Gore, Roopayan Ghosh, Dylan Lewis +1 more

Quantum entanglement is a powerful resource for quantum-enhanced technologies. However, its reliable quantification remains challenging due to the exponential scaling of the Hilbert space with system size, which renders full state tomography infeasible. Moreover, experimentally estimating entanglement typically requires a large number of measurement samples leading to a significant overhead. In this work, we present two models, a feed-forward neural network and an attention-based model, to accurately predict the bipartite second Renyi from projective measurements of quantum states. We benchmark their performance against standard classical shadow estimators and find that the machine-learning approaches achieve higher accuracy and improved sample efficiency across a range of system sizes. Our results demonstrate the potential of machine learning for scalable and efficient estimation of quantum correlations.Quantum entanglement is a powerful resource for quantum-enhanced technologies. However, its reliable quantification remains challenging due to the exponential scaling of the Hilbert space with system size, which renders full state tomography infeasible. Moreover, experimentally estimating entanglement typically requires a large number of measurement samples leading to a significant overhead. In this work, we present two models, a feed-forward neural network and an attention-based model, to accurately predict the bipartite second Renyi from projective measurements of quantum states. We benchmark their performance against standard classical shadow estimators and find that the machine-learning approaches achieve higher accuracy and improved sample efficiency across a range of system sizes. Our results demonstrate the potential of machine learning for scalable and efficient estimation of quantum correlations.

quant-pharXiv:2607.02767Jul 6, 20260 citations

N_A

and

N_B

, with

\mathcal{O}(N_A + N_B)

measurements, and without any prior knowledge of the state. We propose how to experimentally measure the partially transposed moments of a density matrix, and using just the first few of these, extract the negativity via Chebyshev approximation or machine learning techniques. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many body systems in both equilibrium and non-equilibrium regimes.