Quantifying entanglement dimensionality from the quantum Fisher information matrix

• URL: http://arxiv.org/abs/2501.14595v1
• Date: Fri, 24 Jan 2025 16:02:27 GMT
• Title: Quantifying entanglement dimensionality from the quantum Fisher information matrix
• Authors: Shaowei Du, Shuheng Liu, Matteo Fadel, Giuseppe Vitagliano, Qiongyi He,
• Abstract summary: Entanglement is an essential resource for quantum-enhanced metrology. In systems composed by many qudits, it is also important to characterize the dimensionality of entanglement across bipartitions. We fill this gap by deriving a quantum Fisher information matrix (QFIM) criterion for witnessing the entanglement dimensionality across bipartitions.
• Score: 1.747623282473278
• License:
• Abstract: Entanglement is known to be an essential resource for a number of tasks, including quantum-enhanced metrology, and can thus be quantified by figures of merit related to those tasks. In quantum metrology this is emphasized by the connections between the quantum Fisher information (QFI), providing the ultimate bounds of precision, and multipartite entanglement quantifiers such as the depth of entanglement. In systems composed by many qudits, it is also important to characterize the dimensionality of entanglement across bipartitions, i.e., loosely speaking, the minimal number of levels that must be entangled with each other in a given bipartition. However, the impact of high-dimensional entanglement on the QFI remains unexplored. In this work, we fill this gap by deriving a quantum Fisher information matrix (QFIM) criterion for witnessing the entanglement dimensionality across bipartitions, along with scalar corollaries, which we also extend to the multipartite scenario. To further emphasize the significance of our results, we draw connections with the precision of multiparameter estimation, which also provides a practical way of implementing our methods in experiments.

Related papers

• Evaluation of quantum Fisher information for large system [6.706593033554568]
  Quantum Fisher information (QFI) plays a vital role in quantum precision measurement, quantum information, many-body physics, and other domains. This paper presents a methodology for evaluating the QFI of high-dimensional systems by transferring information to an auxiliary system and measuring its sub-QFI.
  arXiv  Detail & Related papers  (2024-08-23T08:50:52Z)
• Effect of the readout efficiency of quantum measurement on the system entanglement [44.99833362998488]
  We quantify the entanglement for a particle on a 1d quantum random walk under inefficient monitoring. We find that the system's maximal mean entanglement at the measurement-induced quantum-to-classical crossover is in different ways by the measurement strength and inefficiency.
  arXiv  Detail & Related papers  (2024-02-29T18:10:05Z)
• Multimodal deep representation learning for quantum cross-platform verification [60.01590250213637]
  Cross-platform verification, a critical undertaking in the realm of early-stage quantum computing, endeavors to characterize the similarity of two imperfect quantum devices executing identical algorithms. We introduce an innovative multimodal learning approach, recognizing that the formalism of data in this task embodies two distinct modalities. We devise a multimodal neural network to independently extract knowledge from these modalities, followed by a fusion operation to create a comprehensive data representation.
  arXiv  Detail & Related papers  (2023-11-07T04:35:03Z)
• Genuine multipartite entanglement measures based on multi-party teleportation capability [2.436414725944717]
  Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing. We define new multipartite entanglement measures for three-qubit systems based on the three-party teleportation capability.
  arXiv  Detail & Related papers  (2022-11-29T07:33:37Z)
• High-dimensional entanglement certification: bounding relative entropy of entanglement in $2d+1$ experiment-friendly measurements [77.34726150561087]
  Entanglement -- the coherent correlations between parties in a quantum system -- is well-understood and quantifiable. Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging. We present a novel certification method whose measurement requirements scale linearly with dimension subsystem.
  arXiv  Detail & Related papers  (2022-10-19T16:52:21Z)
• Scalable approach to many-body localization via quantum data [69.3939291118954]
  Many-body localization is a notoriously difficult phenomenon from quantum many-body physics. We propose a flexible neural network based learning approach that circumvents any computationally expensive step. Our approach can be applied to large-scale quantum experiments to provide new insights into quantum many-body physics.
  arXiv  Detail & Related papers  (2022-02-17T19:00:09Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Quantum Fisher information from randomized measurements [0.0]
  The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas. We use measurements of the density matrix to construct lower bounds that converge to the QFI. We present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.
  arXiv  Detail & Related papers  (2021-05-27T14:16:14Z)
• Computable and operationally meaningful multipartite entanglement measures [0.0]
  Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. We introduce a family of multipartite entanglement measures, called Concentratable Entanglements. We show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test.
  arXiv  Detail & Related papers  (2021-04-14T15:22:56Z)
• Experimental estimation of the quantum Fisher information from randomized measurements [9.795131832414855]
  The quantum Fisher information (QFI) represents a fundamental concept in quantum physics. Here, we explore how the QFI can be estimated via randomized measurements. We experimentally validate this approach using two platforms: a nitrogen-vacancy center spin in diamond and a 4-qubit state provided by a superconducting quantum computer.
  arXiv  Detail & Related papers  (2021-04-01T15:12:31Z)
• Direct estimation of quantum coherence by collective measurements [54.97898890263183]
  We introduce a collective measurement scheme for estimating the amount of coherence in quantum states. Our scheme outperforms other estimation methods based on tomography or adaptive measurements. We show that our method is accessible with today's technology by implementing it experimentally with photons.
  arXiv  Detail & Related papers  (2020-01-06T03:50:42Z)

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.