Optimal approximations of available states and a triple uncertainty relation

• URL: http://arxiv.org/abs/2006.08822v1
• Date: Mon, 15 Jun 2020 23:31:51 GMT
• Title: Optimal approximations of available states and a triple uncertainty relation
• Authors: Xiao-Bin Liang, Bo Li, Liang Huang, Biao-Liang Ye, Shao-Ming Fei, and Shi-Xiang Huang
• Abstract summary: We investigate the optimal convex approximation of the quantum state with respect to a set of available states. We show a concise inequality criterion for decomposing qubit mixed states. Our model and method may be applied to solve similar problems in high-dimensional and multipartite scenarios.
• Score: 8.351713971554405
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the optimal convex approximation of the quantum state with respect to a set of available states. By isometric transformation, we have presented the general mathematical model and its solutions together with a triple uncertainty equality relation. Meanwhile, we show a concise inequality criterion for decomposing qubit mixed states. The new results include previous ones as special cases. Our model and method may be applied to solve similar problems in high-dimensional and multipartite scenarios

Related papers

• High-Probability Bounds for Stochastic Optimization and Variational Inequalities: the Case of Unbounded Variance [59.211456992422136]
  We propose algorithms with high-probability convergence results under less restrictive assumptions. These results justify the usage of the considered methods for solving problems that do not fit standard functional classes in optimization.
  arXiv  Detail & Related papers  (2023-02-02T10:37:23Z)
• Distributed Bayesian Learning of Dynamic States [65.7870637855531]
  The proposed algorithm is a distributed Bayesian filtering task for finite-state hidden Markov models. It can be used for sequential state estimation, as well as for modeling opinion formation over social networks under dynamic environments.
  arXiv  Detail & Related papers  (2022-12-05T19:40:17Z)
• Optimal variance-reduced stochastic approximation in Banach spaces [114.8734960258221]
  We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. We establish non-asymptotic bounds for both the operator defect and the estimation error.
  arXiv  Detail & Related papers  (2022-01-21T02:46:57Z)
• Noncommutative polynomial optimization under symmetry [0.0]
  We present a general framework to exploit the symmetries present in the Navascu'es-Pironio-Ac'in semidefinite relaxations. We put equal emphasis on the moment and sum-of-squares dual approaches.
  arXiv  Detail & Related papers  (2021-12-20T19:02:16Z)
• Variational State and Parameter Estimation [0.8049701904919515]
  This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. A variational approach is used to provide an assumed density which approximates the desired, intractable, distribution. The proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in two numerical examples.
  arXiv  Detail & Related papers  (2020-12-14T05:35:29Z)
• Optimal oracle inequalities for solving projected fixed-point equations [53.31620399640334]
  We study methods that use a collection of random observations to compute approximate solutions by searching over a known low-dimensional subspace of the Hilbert space. We show how our results precisely characterize the error of a class of temporal difference learning methods for the policy evaluation problem with linear function approximation.
  arXiv  Detail & Related papers  (2020-12-09T20:19:32Z)
• Statistical optimality and stability of tangent transform algorithms in logit models [6.9827388859232045]
  We provide conditions on the data generating process to derive non-asymptotic upper bounds to the risk incurred by the logistical optima. In particular, we establish local variation of the algorithm without any assumptions on the data-generating process. We explore a special case involving a semi-orthogonal design under which a global convergence is obtained.
  arXiv  Detail & Related papers  (2020-10-25T05:15:13Z)
• Beyond Worst-Case Analysis in Stochastic Approximation: Moment Estimation Improves Instance Complexity [58.70807593332932]
  We study oracle complexity of gradient based methods for approximation problems. We focus on instance-dependent complexity instead of worst case complexity. Our proposed algorithm and its analysis provide a theoretical justification for the success of moment estimation.
  arXiv  Detail & Related papers  (2020-06-08T09:25:47Z)
• Synchronizing Probability Measures on Rotations via Optimal Transport [26.110033098056334]
  We introduce a new paradigm,textitmeasure synchronization$, for synchronizing graphs with measure-valued uncertainties. In particular, we aim estimating absolute orientations of absolute rotations on a graph on-on-manis.
  arXiv  Detail & Related papers  (2020-04-01T18:44:18Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)
• Lifted Hybrid Variational Inference [31.441922284854893]
  We investigate two approximate lifted variational approaches that are applicable to hybrid domains. We demonstrate that the proposed variational methods are both scalable and can take advantage of approximate model symmetries. We present a sufficient condition for the Bethe approximation to yield a non-trivial estimate over the marginal polytope.
  arXiv  Detail & Related papers  (2020-01-08T22:29:07Z)

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.