Markovian semigroup from mixing non-invertible dynamical maps

• URL: http://arxiv.org/abs/2012.00385v1
• Date: Tue, 1 Dec 2020 10:28:55 GMT
• Title: Markovian semigroup from mixing non-invertible dynamical maps
• Authors: Katarzyna Siudzi\'nska
• Abstract summary: We analyze the convex combinations of non-invertible generalized Pauli dynamical maps. We show how to use non-invertible dynamical maps to produce the Markovian semigroup.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analyze the convex combinations of non-invertible generalized Pauli dynamical maps. By manipulating the mixing parameters, one can produce a channel with shifted singularities, additional singularities, or even no singularities whatsoever. In particular, we show how to use non-invertible dynamical maps to produce the Markovian semigroup. Interestingly, the maps whose mixing results in a semigroup are generated by the time-local generators and time-homogeneous memory kernels that are not regular; i.e., their formulas contain infinities. Finally, we show how the generators and memory kernels change after mixing the corresponding dynamical maps.

Related papers

• Non-Markovian quantum dynamics from symmetric measurements [0.0]
  We use symmetric measurement operators to construct quantum channels that provide a further generalization of generalized Pauli channels. We analyze their important properties, such as complete positivity and the ability to break quantum entanglement.
  arXiv  Detail & Related papers  (2024-02-06T21:26:22Z)
• Discovering Sparse Representations of Lie Groups with Machine Learning [55.41644538483948]
  We show that our method reproduces the canonical representations of the generators of the Lorentz group. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.
  arXiv  Detail & Related papers  (2023-02-10T17:12:05Z)
• Phase-covariant mixtures of non-unital qubit maps [0.0]
  We analyze convex combinations of non-unital qubit maps that are phase-covariant. We show that mixing non-unital channels can result in restoring the unitality, whereas mixing commutative maps can lead to non-commutativity.
  arXiv  Detail & Related papers  (2022-06-21T21:35:17Z)
• Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps [0.0]
  We analyze the connections between the non-Markovianity degree of the most general phase-damping qubit maps and their legitimate mixtures. Using the results for image non-increasing dynamical maps, we formulate the necessary and sufficient conditions for the Pauli maps to satisfy specific divisibility criteria.
  arXiv  Detail & Related papers  (2021-04-13T20:07:03Z)
• Covariant Ergodic Quantum Markov Semigroups via Systems of Imprimitivity [0.0]
  We construct quantum Markov semigroups from covariant completely positive maps. The method is applicable to any fundamental particle, though we demonstrate it for the case of light-like particles.
  arXiv  Detail & Related papers  (2021-02-19T15:32:28Z)
• The Connection between Discrete- and Continuous-Time Descriptions of Gaussian Continuous Processes [60.35125735474386]
  We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining' This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
  arXiv  Detail & Related papers  (2021-01-16T17:11:02Z)
• LieTransformer: Equivariant self-attention for Lie Groups [49.9625160479096]
  Group equivariant neural networks are used as building blocks of group invariant neural networks. We extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups.
  arXiv  Detail & Related papers  (2020-12-20T11:02:49Z)
• Graph Gamma Process Generalized Linear Dynamical Systems [60.467040479276704]
  We introduce graph gamma process (GGP) linear dynamical systems to model real multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a parsimonious set of multivariate sub-sequences. We use the generated random graph, whose number of nonzero-degree nodes is finite, to define both the sparsity pattern and dimension of the latent state transition matrix.
  arXiv  Detail & Related papers  (2020-07-25T04:16:34Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Construction of propagators for divisible dynamical maps [0.0]
  We propose a simple method to construct propagators of dynamical maps using the concept of generalized inverse. We analyze both time-continuous and time-discrete maps.
  arXiv  Detail & Related papers  (2020-04-20T13:13:50Z)
• Distributed, partially collapsed MCMC for Bayesian Nonparametrics [68.5279360794418]
  We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed as, are decomposable into independent sub-measures. We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components. The resulting hybrid algorithm can be applied to allow scalable inference without sacrificing convergence guarantees.
  arXiv  Detail & Related papers  (2020-01-15T23:10:13Z)

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.