Near-optimal pure state estimation with adaptive Fisher-symmetric measurements

• URL: http://arxiv.org/abs/2412.04555v1
• Date: Thu, 05 Dec 2024 19:00:12 GMT
• Title: Near-optimal pure state estimation with adaptive Fisher-symmetric measurements
• Authors: C. Vargas, L. Pereira, A. Delgado,
• Abstract summary: We present a three-stage adaptive method for estimating $d$-dimensional pure quantum states. The total number of measurement outcomes of the method scale linearly as $7d-3$, avoiding the need for collective measurements on multiple copies of the unknown state.
• Score: 0.0
• License:
• Abstract: Quantum state estimation is important for various quantum information processes, including quantum communications, computation, and metrology, which require the characterization of quantum states for evaluation and optimization. We present a three-stage adaptive method for estimating $d$-dimensional pure quantum states using Fisher symmetric measurements (FSM) and a single-shot measurement basis. The result of this measurement is used to generate two FSMs that jointly estimate any pure state up to a null measure set. This estimate is used to adapt a third FMS, which provides the final estimate of the unknown state. Our approach achieves an average estimation infidelity very close to the Gill-Massar lower bound (GMB) without requiring prior information beyond the purity of the unknown state, extending the applicability of FSM to any unknown state. The total number of measurement outcomes of the method scale linearly as $7d-3$, avoiding the need for collective measurements on multiple copies of the unknown state. This work highlights the potential of adaptive estimation techniques in quantum state characterization while maintaining efficiency in the number of measurement outcomes.

Related papers

• Randomized measurements for multi-parameter quantum metrology [0.0]
  We show that randomized measurements perform near-optimally when estimating an arbitrary number of parameters in pure states. The near-optimality is also shown in estimating the maximal number of parameters for three types of mixed states that are well-conditioned on its support.
  arXiv  Detail & Related papers  (2025-02-05T19:00:04Z)
• The Cramér-Rao approach and global quantum estimation of bosonic states [52.47029505708008]
  It is unclear whether the Cram'er-Rao approach is applicable for global estimation instead of local estimation. We find situations where the Cram'er-Rao approach does and does not work for quantum state estimation problems involving a family of bosonic states in a non-IID setting.
  arXiv  Detail & Related papers  (2024-09-18T09:49:18Z)
• Metrological power of incompatible measurements [0.8488455943441637]
  We show that measurement incompatibility is a necessary resource to enhance the precision of quantum metrology. We propose a probabilistic method of operational quasiprobability (OQ) consisting of the measuring averages. We prove that Fisher information (FI), based on positive OQ, can be larger than the conventional quantum FI.
  arXiv  Detail & Related papers  (2023-11-20T14:10:41Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system. This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Estimating many properties of a quantum state via quantum reservoir processing [2.5432391525687748]
  We propose a general framework for constructing classical approximations of arbitrary quantum states with quantum reservoirs. A key advantage of our method is that only a single local measurement setting is required for estimating arbitrary properties. This estimation scheme is extendable to higher-dimensional systems and hybrid systems with non-identical local dimensions.
  arXiv  Detail & Related papers  (2023-05-11T15:21:21Z)
• Quantum-enhanced mean value estimation via adaptive measurement [0.39102514525861415]
  Mean value estimation of observables is an essential subroutine in quantum computing algorithms. The quantum estimation theory identifies the ultimate precision of such an estimator, which is referred to as the quantum Cram'er-Rao (QCR) lower bound or equivalently the inverse of the quantum Fisher information. We propose a quantum-enhanced mean value estimation method in a depolarizing noisy environment that saturates the QCR bound in the limit of a large number of qubits.
  arXiv  Detail & Related papers  (2022-10-27T17:13:07Z)
• Potential and limitations of quantum extreme learning machines [55.41644538483948]
  We present a framework to model QRCs and QELMs, showing that they can be concisely described via single effective measurements. Our analysis paves the way to a more thorough understanding of the capabilities and limitations of both QELMs and QRCs.
  arXiv  Detail & Related papers  (2022-10-03T09:32:28Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Performance of the quantum MaxEnt estimation in the presence of physical symmetries [0.0]
  We study the performance of the MaxEnt method for quantum state estimation when there is prior information about symmetries of the unknown state. We implement this algorithm to carry out numerical simulations estimating the density matrix of several three-qubit states of particular interest for quantum information tasks.
  arXiv  Detail & Related papers  (2021-09-22T15:56:17Z)
• In and out of equilibrium quantum metrology with mean-field quantum criticality [68.8204255655161]
  We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level.
  arXiv  Detail & Related papers  (2020-01-09T19:20:42Z)
• 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.