Accessible maps in a group of classical or quantum channels

• URL: http://arxiv.org/abs/2201.12524v1
• Date: Sat, 29 Jan 2022 08:06:21 GMT
• Title: Accessible maps in a group of classical or quantum channels
• Authors: Koorosh Sadri, Fereshte Shahbeigi, Zbigniew Pucha{\l}a, Karol \.Zyczkowski
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 structure of the closure of the analyzed group $G$ plays a pivotal role in this regard. The set of all convex combinations of the group elements contains a subset of channels that are accessible by a dynamical semigroup. We demonstrate that accessible channels are determined by probability vectors of weights of a convex combination of the group elements, which depend neither on the dimension of the space on which the channels act, nor on the specific representation of the group. Investigating geometric properties of the set $\mathcal{A}$ of accessible maps we show that this set is non-convex, but it enjoys the star-shape property with respect to the uniform mixture of all elements of the group. We demonstrate that the set $\mathcal{A}$ covers a positive volume in the polytope of all convex combinations of the elements of the group.

Related papers

• Weyl channels for multipartite systems [42.37986459997699]
  Quantum channels describe unitary and non-unitary evolution of quantum systems. We show that these channels are completely characterized by elements drawn of finite cyclic groups.
  arXiv  Detail & Related papers  (2023-10-17T02:45:47Z)
• Instance-Optimal Cluster Recovery in the Labeled Stochastic Block Model [79.46465138631592]
  We devise an efficient algorithm that recovers clusters using the observed labels. We present Instance-Adaptive Clustering (IAC), the first algorithm whose performance matches these lower bounds both in expectation and with high probability.
  arXiv  Detail & Related papers  (2023-06-18T08:46:06Z)
• Group-covariant extreme and quasi-extreme channels [0.0]
  We introduce a systematic approach that enables us to construct exactly those extreme channels that are covariant with respect to a finite discrete group or a compact connected Lie group. We formalize the problem of constructing and classifying group-covariant generalized extreme channels, thereby yielding an algorithmic approach to solving, which we express as pseudocode.
  arXiv  Detail & Related papers  (2022-10-07T10:43:19Z)
• Pauli component erasing quantum channels [58.720142291102135]
  We propose a family of quantum maps that preserve or completely erase the components of a multi-qubit system. For the corresponding channels, it is shown that the preserved components can be interpreted as a finite vector subspace. We show that the obtained family of channels forms a semigroup and derive its generators.
  arXiv  Detail & Related papers  (2022-05-12T00:11:43Z)
• Noninvertibility as a requirement for creating a semigroup under convex combinations of channels [0.0]
  We find that mixing only semigroups can never produce a semigroup. For a convex combination to yield a semigroup, most of the input channels have to be noninvertible.
  arXiv  Detail & Related papers  (2021-11-17T17:52:42Z)
• A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups [115.58550697886987]
  We provide a completely general algorithm for solving for the equivariant layers of matrix groups. In addition to recovering solutions from other works as special cases, we construct multilayer perceptrons equivariant to multiple groups that have never been tackled before. Our approach outperforms non-equivariant baselines, with applications to particle physics and dynamical systems.
  arXiv  Detail & Related papers  (2021-04-19T17:21:54Z)
• 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)
• Constraints on Maximal Entanglement Under Groups of Permutations [73.21730086814223]
  Sets of entanglements are inherently equal, lying in the same orbit under the group action. We introduce new, generalized relationships for the maxima of those entanglement by exploiting the normalizer and normal subgroups of the physical symmetry group.
  arXiv  Detail & Related papers  (2020-11-30T02:21:22Z)
• On construction of finite averaging sets for $SL(2, \mathbb{C})$ via its Cartan decomposition [0.0]
  Averaging physical quantities over Lie groups appears in many contexts like quantum information science or quantum optics. In this work we investigate the problem of constructing finite averaging sets for averaging over general non-compact matrix Lie groups. We provide an explicit calculation of such sets for the group $SL(2, mathbbC)$, although our construction can be applied to other cases.
  arXiv  Detail & Related papers  (2020-10-29T17:26:33Z)
• Log-Convex set of Lindblad semigroups acting on $N$-level system [0.0]
  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.
  arXiv  Detail & Related papers  (2020-03-26T23:24:47Z)
• 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.