Approximating Invertible Maps by Recovery Channels: Optimality and an Application to Non-Markovian Dynamics

• URL: http://arxiv.org/abs/2111.02975v2
• Date: Mon, 4 Apr 2022 16:09:44 GMT
• Title: Approximating Invertible Maps by Recovery Channels: Optimality and an Application to Non-Markovian Dynamics
• Authors: Lea Lautenbacher, Fernando de Melo and Nadja K. Bernardes
• Abstract summary: We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing and amplitude damping. We extend this idea to explore the use of recovery maps as an approximation of inverse maps, and apply it in the context of non-Markovian dynamics.
• Score: 68.8204255655161
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing and amplitude damping. We illustrate how well a physically implementable recovery map simulates an inverse evolution. We extend this idea to explore the use of recovery maps as an approximation of inverse maps, and apply it in the context of non-Markovian dynamics. We show how this strategy attenuates non-Markovian effects, such as the backflow of information.

Related papers

• Exploring the Non-Markovian Dynamics in Depolarizing Maps [0.0]
  The study brings together the various ways to identify and quantify non-Markovianity. The trajectories traced during evolution, demonstrate the loss of CP-divisibility and the emergence of non-Markovianity.
  arXiv  Detail & Related papers  (2024-03-07T04:59:58Z)
• Recovering complete positivity of non-Markovian quantum dynamics with Choi-proximity regularization [0.5461938536945721]
  A relevant problem in the theory of open quantum systems is the lack of complete positivity of dynamical maps obtained after weak-coupling approximations. We propose a numerical method to cure the complete-positivity violation issue while preserving the non-Markovian features of an arbitrary original dynamical map.
  arXiv  Detail & Related papers  (2023-09-28T10:29:43Z)
• Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Models [24.5360032541275]
  Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. Our key observation is that most existing inverse problem solvers lack the ability to adapt their compute power to the difficulty of the reconstruction task. We propose a novel method, $textitseverity encoding$, to estimate the degradation severity of corrupted signals in the latent space of an autoencoder.
  arXiv  Detail & Related papers  (2023-09-12T23:41:29Z)
• Subject-specific quantitative susceptibility mapping using patch based deep image priors [13.734472448148333]
  We propose a subject-specific, patch-based, unsupervised learning algorithm to estimate the susceptibility map. We make the problem well-posed by exploiting the redundancies across the patches of the map using a deep convolutional neural network. We tested the algorithm on a 3D invivo dataset and demonstrated improved reconstructions over competing methods.
  arXiv  Detail & Related papers  (2022-10-10T02:28:53Z)
• Towards performant and reliable undersampled MR reconstruction via diffusion model sampling [67.73698021297022]
  DiffuseRecon is a novel diffusion model-based MR reconstruction method. It guides the generation process based on the observed signals. It does not require additional training on specific acceleration factors.
  arXiv  Detail & Related papers  (2022-03-08T02:25:38Z)
• ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer [60.27951773998535]
  We propose a recurrent transformer model, namely textbfReconFormer, for MRI reconstruction. It can iteratively reconstruct high fertility magnetic resonance images from highly under-sampled k-space data. We show that it achieves significant improvements over the state-of-the-art methods with better parameter efficiency.
  arXiv  Detail & Related papers  (2022-01-23T21:58:19Z)
• CAMERAS: Enhanced Resolution And Sanity preserving Class Activation Mapping for image saliency [61.40511574314069]
  Backpropagation image saliency aims at explaining model predictions by estimating model-centric importance of individual pixels in the input. We propose CAMERAS, a technique to compute high-fidelity backpropagation saliency maps without requiring any external priors.
  arXiv  Detail & Related papers  (2021-06-20T08:20:56Z)
• Learning landmark geodesics using Kalman ensembles [0.0]
  We study the problem of diffeomorphometric geodesic landmark matching. The objective is to find a diffeomorphism that via its group action maps between two sets of landmarks.
  arXiv  Detail & Related papers  (2021-03-25T18:52:01Z)
• A Transfer Learning approach to Heatmap Regression for Action Unit intensity estimation [50.261472059743845]
  Action Units (AUs) are geometrically-based atomic facial muscle movements. We propose a novel AU modelling problem that consists of jointly estimating their localisation and intensity. A Heatmap models whether an AU occurs or not at a given spatial location.
  arXiv  Detail & Related papers  (2020-04-14T16:51:13Z)
• Solving Inverse Problems with a Flow-based Noise Model [100.18560761392692]
  We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns.
  arXiv  Detail & Related papers  (2020-03-18T08:33:49Z)

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.