Peripherally automorphic unital completely positive maps

• URL: http://arxiv.org/abs/2212.07351v1
• Date: Wed, 14 Dec 2022 17:25:51 GMT
• Title: Peripherally automorphic unital completely positive maps
• Authors: B. V. Rajarama Bhat, Samir Kar and Bharat Talwar
• Abstract summary: We analyze a decomposition of general UCP maps in finite dimensions into persistent and transient parts. It is shown that UCP maps on finite dimensional $C*$-algebras with spectrum contained in the unit circle are $ast$-automorphisms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We identify and characterize unital completely positive (UCP) maps on finite dimensional $C^*$-algebras for which the Choi-Effros product extended to the space generated by peripheral eigenvectors matches with the original product. We analyze a decomposition of general UCP maps in finite dimensions into persistent and transient parts. It is shown that UCP maps on finite dimensional $C^*$-algebras with spectrum contained in the unit circle are $\ast$-automorphisms.

Related papers

• Spectral radii for subsets of Hilbert $C^*$-modules and spectral properties of positive maps [0.0]
  A Rota-Strang type characterisation is proved for the joint spectral radius. An approximation result for the joint spectral radius in terms of the outer spectral radius has been established.
  arXiv  Detail & Related papers  (2024-05-23T19:28:05Z)
• Characterizations of homomorphisms among unital completely positive maps [0.0]
  We prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if its adjusted Choi operator is a projection. Both equivalences generalize familiar facts about maps between finite sets.
  arXiv  Detail & Related papers  (2024-03-12T00:55:44Z)
• From the Choi Formalism in Infinite Dimensions to Unique Decompositions of Generators of Completely Positive Dynamical Semigroups [0.0]
  We prove that there exists a unique bounded operator $K$ and a unique completely positive map $Phi$ in any Hilbert space. In particular, we find examples of positive semi-definite operators which have empty pre-image under the Choi formalism as soon as the underlying Hilbert space is infinite-dimensional.
  arXiv  Detail & Related papers  (2024-01-25T17:44:14Z)
• Degradable Strongly Entanglement Breaking Maps [0.0]
  We prove that unital degradable entanglement breaking maps are precisely the $C*$-extreme points of the convex set of unital entanglement breaking maps on matrix algebras.
  arXiv  Detail & Related papers  (2023-04-01T13:14:27Z)
• Unextendibility, uncompletability, and many-copy indistinguishable ensembles [49.1574468325115]
  We show that the complement of any bipartite pure entangled state is spanned by product states which form a nonorthogonal unextendible product basis (nUPB) of maximum cardinality. We also report a class of multipartite many-copy indistinguishable ensembles for which local indistinguishability property increases with decreasing number of mixed states.
  arXiv  Detail & Related papers  (2023-03-30T16:16:41Z)
• 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)
• Efficient displacement convex optimization with particle gradient descent [57.88860627977882]
  Particle gradient descent is widely used to optimize functions of probability measures. This paper considers particle gradient descent with a finite number of particles and establishes its theoretical guarantees to optimize functions that are emphdisplacement convex in measures.
  arXiv  Detail & Related papers  (2023-02-09T16:35:59Z)
• Reinforcement Learning from Partial Observation: Linear Function Approximation with Provable Sample Efficiency [111.83670279016599]
  We study reinforcement learning for partially observed decision processes (POMDPs) with infinite observation and state spaces. We make the first attempt at partial observability and function approximation for a class of POMDPs with a linear structure.
  arXiv  Detail & Related papers  (2022-04-20T21:15:38Z)
• Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps [0.0]
  We study the convex combinations of the $(d+1)$ generalized Pauli dynamical maps in a Hilbert space of dimension $d$. For certain choices of the decoherence function, the maps are noninvertible and they remain under convex combinations as well.
  arXiv  Detail & Related papers  (2022-01-10T10:21:10Z)
• The PPT$^2$ conjecture holds for all Choi-type maps [1.5229257192293197]
  We prove that the PPT$2$ conjecture holds for linear maps between matrix algebras which are covariant under the action of the diagonal unitary group. Our proof relies on a generalization of the matrix-theoretic notion of factor width for pairwise completely positive matrices, and a complete characterization in the case of factor width two.
  arXiv  Detail & Related papers  (2020-11-07T17:00:22Z)
• A deep network construction that adapts to intrinsic dimensionality beyond the domain [79.23797234241471]
  We study the approximation of two-layer compositions $f(x) = g(phi(x))$ via deep networks with ReLU activation. We focus on two intuitive and practically relevant choices for $phi$: the projection onto a low-dimensional embedded submanifold and a distance to a collection of low-dimensional sets.
  arXiv  Detail & Related papers  (2020-08-06T09:50:29Z)
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps [91.3755431537592]
  We show that any positive product of a qubit map with itself is decomposable. We characterize the cone of decomposable ququart Pauli diagonal maps.
  arXiv  Detail & Related papers  (2020-06-25T16:39:32Z)
• 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.