Log-Convex set of Lindblad semigroups acting on $N$-level system

• URL: http://arxiv.org/abs/2003.12184v1
• Date: Thu, 26 Mar 2020 23:24:47 GMT
• Title: Log-Convex set of Lindblad semigroups acting on $N$-level system
• Authors: Fereshte Shahbeigi (1 and 2), David Amaro-Alcal\'a (3), Zbigniew Pucha{\l}a (4 and 5), Karol \.Zyczkowski (5 and 6 and 7) ((1) Department of Physics Ferdowsi University of Mashhad Mashhad Iran, (2) Department of Physics Sharif University of Technology Tehran Iran, (3) Instituto de F\'isica Universidad Nacional Aut\'onoma de M\'exico Mexico City Mexico, (4) Institute of Theoretical and Applied Informatics Polish Academy of Sciences Poland, (5) Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Krakow Poland, (6) Center for Theoretical Physics Polish Academy of Sciences Warszawa Poland (7) National Quantum Information Centre University of Gdansk Poland)
• Abstract summary: We analyze the set $cal A_NQ$ of mixed unitary channels represented in the Weyl basis. We show that for mixed Weyl channels the hyper-decoherence commutes with the dynamics. We demonstrate that the set $cal A_3Q$ is included in the set $cal UQ_3$ of quantum unistochastic channels.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analyze the set ${\cal A}_N^Q$ of mixed unitary channels represented in the Weyl basis and accessible by a Lindblad semigroup acting on an $N$-level quantum system. General necessary and sufficient conditions for a mixed Weyl quantum channel of an arbitrary dimension to be accessible by a semigroup are established. The set ${\cal A}_N^Q$ is shown to be log--convex and star-shaped with respect to the completely depolarizing channel. A decoherence supermap acting in the space of Lindblad operators transforms them into the space of Kolmogorov generators of classical semigroups. We show that for mixed Weyl channels the hyper-decoherence commutes with the dynamics, so that decohering a quantum accessible channel we obtain a bistochastic matrix form the set ${\cal A}_N^C$ of classical maps accessible by a semigroup. Focusing on $3$-level systems we investigate the geometry of the sets of quantum accessible maps, its classical counterpart and the support of their spectra. We demonstrate that the set ${\cal A}_3^Q$ is not included in the set ${\cal U}^Q_3$ of quantum unistochastic channels, although an analogous relation holds for $N=2$. The set of transition matrices obtained by hyper-decoherence of unistochastic channels of order $N\ge 3$ is shown to be larger than the set of unistochastic matrices of this order, and yields a motivation to introduce the larger sets of $k$-unistochastic matrices.

Related papers

• Fermionic parton theory of Rydberg $\mathbb{Z}_2$ quantum spin liquids [0.0]
  We describe the symmetry fractionalization patterns in a topologically ordered $mathbbZ_2$ quantum spin liquid (QSL) We also present detailed analyses of the dynamical structure factors as a reference for future experiments.
  arXiv  Detail & Related papers  (2024-09-25T18:00:00Z)
• Tensor network approximation of Koopman operators [0.0]
  We propose a framework for approximating the evolution of observables of measure-preserving ergodic systems. Our approach is based on a spectrally-convergent approximation of the skew-adjoint Koopman generator. A key feature of this quantum-inspired approximation is that it captures information from a tensor product space of dimension $(2d+1)n$.
  arXiv  Detail & Related papers  (2024-07-09T21:40:14Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates [53.66705737169404]
  We consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets. Our main findings are that the maximum number of messages thus identifiable scales super-exponentially as $2R,nlog n$ with the block length $n$. Results are shown to generalise directly to classical-quantum channels with finite-dimensional output quantum system.
  arXiv  Detail & Related papers  (2024-02-14T11:59:30Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• Accessible maps in a group of classical or quantum channels [0.0]
  We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the closure of the analyzed group $G structure are studied.
  arXiv  Detail & Related papers  (2022-01-29T08:06:21Z)
• Reachable sets for two-level open quantum systems driven by coherent and incoherent controls [77.34726150561087]
  We study controllability in the set of all density matrices for a two-level open quantum system driven by coherent and incoherent controls. For two coherent controls, the system is shown to be completely controllable in the set of all density matrices.
  arXiv  Detail & Related papers  (2021-09-09T16:14:23Z)
• Quantum and classical dynamical semigroups of superchannels and semicausal channels [0.0]
  A superchannel is a linear map that maps quantum channels to quantum channels. No useful constructive characterization of the generators of such semigroups is known. We derive a normal for these generators using a novel technique.
  arXiv  Detail & Related papers  (2021-09-08T18:01:17Z)
• Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states [0.0]
  General physical background of Peres-Horodecki positive partial transpose (ppt-) separability criterion is revealed. C causal separability criterion has been proposed for arbitrary $ DN times DN$ density matrices acting in $ mathcalH_Dotimes N $ Hilbert spaces.
  arXiv  Detail & Related papers  (2020-12-17T07:37:30Z)
• SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS [55.41644538483948]
  Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projectedangled Pair States (PEPS) Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence.
  arXiv  Detail & Related papers  (2019-12-31T16:30:25Z)

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.