Resource-efficient Direct Characterization of General Density Matrix

• URL: http://arxiv.org/abs/2303.06903v2
• Date: Sun, 14 Jul 2024 05:03:42 GMT
• Title: Resource-efficient Direct Characterization of General Density Matrix
• Authors: Liang Xu, Mingti Zhou, Runxia Tao, Zhipeng Zhong, Ben Wang, Zhiyong Cao, Hongkuan Xia, Qianyi Wang, Hao Zhan, Aonan Zhang, Shang Yu, Nanyang Xu, Ying Dong, Changliang Ren, Lijian Zhang,
• Abstract summary: Sequential weak measurements allow the direct extraction of individual density-matrix elements instead of globally reconstructing the whole density matrix. We propose a resource-efficient scheme (RES) to directly characterize the density matrix of general multi-qudit systems. We experimentally apply the RES to the direct characterization of general single-photon qutrit states and two-photon entangled states.
• Score: 10.147208307495442
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sequential weak measurements allow the direct extraction of individual density-matrix elements instead of globally reconstructing the whole density matrix, opening a new avenue for the characterization of quantum systems. Nevertheless, the requirement of multiple coupling for each qudit of quantum systems and the lack of appropriate precision evaluation constraint its applicability extension, especially for multi-qudit quantum systems. Here, we propose a resource-efficient scheme (RES) to directly characterize the density matrix of general multi-qudit systems, which not only optimizes the measurements but also establishes a feasible estimation analysis. In this scheme, an efficient observable of quantum system is constructed such that a single meter state coupled to each qudit is sufficient to extract the corresponding density-matrix element. An appropriate model based on the statistical distribution of errors are used to evaluate the precision and feasibility of the scheme. We experimentally apply the RES to the direct characterization of general single-photon qutrit states and two-photon entangled states. The results show that the RES outperforms the sequential schemes in terms of efficiency and precision in both weak- and strong- coupling scenarios. This work sheds new light on the practical characterization of large-scale quantum systems and investigation of their non-classical properties.

Related papers

• Time-bin entanglement in the deterministic generation of linear photonic cluster states [0.0]
  We theoretically investigate strategies for the deterministic creation of trains of time-bin entangled photons using an individual quantum emitter. We show the theoretical generation of linear cluster states with substantial numbers of entangled photonic qubits in full microscopic numerical simulations.
  arXiv  Detail & Related papers  (2024-03-13T13:38:45Z)
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling [49.1574468325115]
  A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics. We establish that scaling predictions are matched by a privileged process, and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all timescales.
  arXiv  Detail & Related papers  (2023-10-17T15:41:50Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
  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)
• Informationally complete measures of quantum entanglement [0.0]
  We introduce a family of entanglement measures which are given by the complete eigenvalues of the reduced density matrices of the system. It is demonstrated that such ICEMs can characterize finer and distinguish better the entanglement than existing well-known entanglement measures.
  arXiv  Detail & Related papers  (2022-06-22T19:27:07Z)
• Regression of high dimensional angular momentum states of light [47.187609203210705]
  We present an approach to reconstruct input OAM states from measurements of the spatial intensity distributions they produce. We showcase our approach in a real photonic setup, generating up-to-four-dimensional OAM states through a quantum walk dynamics.
  arXiv  Detail & Related papers  (2022-06-20T16:16:48Z)
• System Identification via Nuclear Norm Regularization [44.9687872697492]
  This paper studies the problem of identifying low-order linear systems via Hankel nuclear norm regularization. We provide novel statistical analysis for this regularization and carefully contrast it with the unregularized ordinary least-squares (OLS) estimator.
  arXiv  Detail & Related papers  (2022-03-30T20:56:27Z)
• Quantum Optimal Control for Pure-State Preparation Using One Initial State [0.0]
  This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. We consider the case where a number of qubits are dispersively coupled to a readout cavity.
  arXiv  Detail & Related papers  (2021-06-16T21:49:48Z)
• Reduced Density Matrix Sampling: Self-consistent Embedding and Multiscale Electronic Structure on Current Generation Quantum Computers [1.3488660476261511]
  We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers. We show that these self-consistent algorithms are indeed highly robust, even in the presence of significant noises on quantum hardware.
  arXiv  Detail & Related papers  (2021-04-12T14:57:51Z)
• Optimal Entanglement Certification from Moments of the Partial Transpose [2.9475513512647455]
  We propose two general entanglement detection methods based on the moments of the partially transposed density matrix. The first method is based on the Hankel matrices and provides a family of entanglement criteria. The second method is optimal and gives necessary and sufficient conditions for entanglement based on some moments of the partially transposed density matrix.
  arXiv  Detail & Related papers  (2021-03-11T19:00:03Z)
• Learning with Density Matrices and Random Features [44.98964870180375]
  A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems. This paper explores how density matrices can be used as a building block for machine learning models.
  arXiv  Detail & Related papers  (2021-02-08T17:54:59Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)

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.