Concrete Quantum Channels and Algebraic Structure of Abstract Quantum Channels

• URL: http://arxiv.org/abs/2305.11471v2
• Date: Fri, 15 Mar 2024 15:11:24 GMT
• Title: Concrete Quantum Channels and Algebraic Structure of Abstract Quantum Channels
• Authors: M. N. N. Namboodiri,
• Abstract summary: An attempt is made to identify generalized invertible channels and also the idempotent channels. The motivation behind this study is its applicability to the reversibility of channel transformations. This is related to the coding-encoding problem in quantum information theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This article analyzes the algebraic structure of the set of all quantum channels and its subset consisting of quantum channels that have Holevo representation. The regularity of these semigroups under composition of mappings are analysed. It is also known that these sets are compact convex sets and, therefore, rich in geometry. An attempt is made to identify generalized invertible channels and also the idempotent channels. When channels are of the Holevo type, these two problems are fully studied in this article. The motivation behind this study is its applicability to the reversibility of channel transformations and recent developments in resource-destroying channels, which are idempotents. This is related to the coding-encoding problem in quantum information theory. Several examples are provided, with the main examples coming from pre-conditioner maps which assigns preconditioners to matrices, in numerical linear algebra.Thus the known pre-conditioner maps are viewd as a quantum-channel in finite dimentions.

Related papers

• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• 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)
• Normal quantum channels and Markovian correlated two-qubit quantum errors [77.34726150561087]
  We study general normally'' distributed random unitary transformations. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process.
  arXiv  Detail & Related papers  (2023-07-25T15:33:28Z)
• Entanglement Breaking Rank via Complementary Channels and Multiplicative Domains [4.588028371034406]
  We introduce a new technique to determine if a channel is entanglement breaking and to evaluate entanglement breaking rank. We show the entanglement breaking and Choi ranks of such channels are equal.
  arXiv  Detail & Related papers  (2022-11-21T23:33:10Z)
• A Complete Equational Theory for Quantum Circuits [58.720142291102135]
  We introduce the first complete equational theory for quantum circuits. Two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations.
  arXiv  Detail & Related papers  (2022-06-21T17:56:31Z)
• 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)
• The platypus of the quantum channel zoo [12.4245398967236]
  We study a simple, low-dimensional family of quantum channels with exotic quantum information-theoretic features. We generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior.
  arXiv  Detail & Related papers  (2022-02-16T23:54:07Z)
• 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)
• Coherent control and distinguishability of quantum channels via PBS-diagrams [59.94347858883343]
  We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS) We characterise the observational equivalence of purified channels in various coherent-control contexts, paving the way towards a faithful representation of quantum channels under coherent control.
  arXiv  Detail & Related papers  (2021-03-02T22:56:25Z)
• Divisibility classes of qubit maps and singular Gaussian channels [0.0]
  In the first project we study quantum channels, which are the most general operations mapping quantum states into quantum states. In the second project we study the functional forms of one-mode Gaussian quantum channels in the position state representation.
  arXiv  Detail & Related papers  (2020-09-01T00:53:47Z)

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.