Quantifying Subspace Entanglement with Geometric Measures

• URL: http://arxiv.org/abs/2311.10353v1
• Date: Fri, 17 Nov 2023 06:54:48 GMT
• Title: Quantifying Subspace Entanglement with Geometric Measures
• Authors: Xuanran Zhu, Chao Zhang, and Bei Zeng
• Abstract summary: We introduce a measure of $r$-bounded rank, $E_r(S)ite, for a given subspace. It sheds light on the subspace's ability to preserve entanglement. It is useful in validating highly entangled subspaces in bipartite systems.
• Score: 4.347947462145898
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Determining whether a quantum subspace is entangled and quantifying its entanglement level remains a fundamental challenge in quantum information science. This paper introduces a geometric measure of $r$-bounded rank, $E_r(S)$, for a given subspace $S$. This measure, derived from the established geometric measure of entanglement, is tailored to assess the entanglement within $S$. It not only provides a benchmark for quantifying the entanglement level but also sheds light on the subspace's ability to preserve such entanglement. Utilizing non-convex optimization techniques from the domain of machine learning, our method effectively calculates $E_r(S)$ in various scenarios. Showcasing strong performance in comparison to existing hierarchical and PPT relaxation techniques, our approach is notable for its accuracy, computational efficiency, and wide-ranging applicability. This versatile and effective tool paves the way for numerous new applications in quantum information science. It is particularly useful in validating highly entangled subspaces in bipartite systems, determining the border rank of multipartite states, and identifying genuinely or completely entangled subspaces. Our approach offers a fresh perspective for quantifying entanglement, while also shedding light on the intricate structure of quantum entanglement.

Related papers

• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls [77.34726150561087]
  The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. We adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem.
  arXiv  Detail & Related papers  (2023-07-17T13:37:18Z)
• Reduced basis surrogates for quantum spin systems based on tensor networks [0.0]
  We show how a greedy strategy to assemble the reduced basis can be implemented. observables required for the computation of phase diagrams can be computed independent of the underlying Hilbert space. We illustrate the efficiency and accuracy of this approach for different one-dimensional quantum spin-1 models, including anisotropic as well as biquadratic exchange interactions.
  arXiv  Detail & Related papers  (2023-04-26T14:29:58Z)
• Tight Cram\'{e}r-Rao type bounds for multiparameter quantum metrology through conic programming [61.98670278625053]
  It is paramount to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. Here, we give a concrete way to find uncorrelated measurement strategies with optimal precisions. We show numerically that there is a strict gap between the previous efficiently computable bounds and the ultimate precision bound.
  arXiv  Detail & Related papers  (2022-09-12T13:06:48Z)
• Computationally Efficient PAC RL in POMDPs with Latent Determinism and Conditional Embeddings [97.12538243736705]
  We study reinforcement learning with function approximation for large-scale Partially Observable Decision Processes (POMDPs) Our algorithm provably scales to large-scale POMDPs.
  arXiv  Detail & Related papers  (2022-06-24T05:13:35Z)
• A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems [0.0]
  We construct surrogate models for quantification uncertainty (UQ) on complex partial differential equations (PPDEs) The curse of dimensionality can be a pre-dimensional subspace used with suitable unsupervised learning techniques. We demonstrate both the advantages and limitations of a suitable m-PCE model and we conclude that a suitable m-PCE model provides a cost-effective approach to deep subspaces.
  arXiv  Detail & Related papers  (2022-02-09T16:33:40Z)
• Optimal classical and quantum real and complex dimension witness [0.0]
  We use the linear independence tested by a determinant as a dimension certificate. We discuss the practical application of the test to certify the space logical operations on a quantum computer.
  arXiv  Detail & Related papers  (2022-02-07T14:11:40Z)
• Quantum state tomography as a numerical optimization problem [0.0]
  We show that a set of projectors on half-dimensional subspaces can be arranged in an informationally optimal fashion for quantum state tomography. We find that in dimension six such a set of mutually-unbiased subspaces can be approximated with a deviation irrelevant for practical applications.
  arXiv  Detail & Related papers  (2020-12-28T21:32:34Z)
• Experimental characterization of quantum processes: a selective and efficient method in arbitrary finite dimension [0.0]
  We show how to implement an algorithm to selectively and efficiently estimate any parameter characterizing a quantum process in a non-prime power dimension. We conducted for the first time an experimental verification of the algorithm in a Hilbert space of dimension $d=6$.
  arXiv  Detail & Related papers  (2020-11-16T19:14:56Z)
• Joint and Progressive Subspace Analysis (JPSA) with Spatial-Spectral Manifold Alignment for Semi-Supervised Hyperspectral Dimensionality Reduction [48.73525876467408]
  We propose a novel technique for hyperspectral subspace analysis. The technique is called joint and progressive subspace analysis (JPSA) Experiments are conducted to demonstrate the superiority and effectiveness of the proposed JPSA on two widely-used hyperspectral datasets.
  arXiv  Detail & Related papers  (2020-09-21T16:29:59Z)
• Learnable Subspace Clustering [76.2352740039615]
  We develop a learnable subspace clustering paradigm to efficiently solve the large-scale subspace clustering problem. The key idea is to learn a parametric function to partition the high-dimensional subspaces into their underlying low-dimensional subspaces. To the best of our knowledge, this paper is the first work to efficiently cluster millions of data points among the subspace clustering methods.
  arXiv  Detail & Related papers  (2020-04-09T12:53:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.