Related papers: Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras

Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras

URL: http://arxiv.org/abs/2402.15440v5
Date: Tue, 12 Nov 2024 08:50:53 GMT
Title: Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras
Authors: Cédric Arhancet,
Abstract summary: We investigate a new class of unital quantum computation channels on $mathrmM_2k$. We identify the matrix algebra $mathrmM_2k$ with a finite-dimensional fermion algebra. Our calculations yield exact values applicable to the operators of the fermionic Ornstein-Uhlenbeck semigroup.
Score: 0.0
License:
Abstract: We investigate a new class of unital quantum channels on $\mathrm{M}_{2^k}$, acting as radial multipliers when we identify the matrix algebra $\mathrm{M}_{2^k}$ with a finite-dimensional fermion algebra. Our primary contribution lies in the precise computation of the (optimal) rate at which classical information can be transmitted through these channels from a sender to a receiver when they share an unlimited amount of entanglement. Our approach relies on new connections between fermion algebras with the $n$-dimensional discrete hypercube $\{-1,1\}^n$. Significantly, our calculations yield exact values applicable to the operators of the fermionic Ornstein-Uhlenbeck semigroup. This advancement not only provides deeper insights into the structure and behaviour of these channels but also enhances our understanding of Quantum Information Theory in a dimension-independent context.

Related papers

Concentration of quantum channels with random Kraus operators via matrix Bernstein inequality [0.5439020425818999]
We generate quantum channels with random Kraus operators to typically obtain almost twirling quantum channels and quantum expanders. To prove the concentration phenomena, we use matrix Bernstein's inequality. New non-unital model of super-operators generated by bounded and isotropic random Kraus operators was introduced.
arXiv Detail & Related papers (2024-09-10T20:55:15Z)
Volichenko-type metasymmetry of braided Majorana qubits [0.0]
This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits. Mixed-bracket Heisenberg-Lie algebras are introduced.
arXiv Detail & Related papers (2024-06-02T21:50:29Z)
Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
arXiv Detail & Related papers (2023-05-22T11:00:25Z)
Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z)
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)
Quantum teleportation in the commuting operator framework [63.69764116066747]
We present unbiased teleportation schemes for relative commutants $N'cap M$ of a large class of finite-index inclusions $Nsubseteq M$ of tracial von Neumann algebras. We show that any tight teleportation scheme for $N$ necessarily arises from an orthonormal unitary Pimsner-Popa basis of $M_n(mathbbC)$ over $N'$.
arXiv Detail & Related papers (2022-08-02T00:20:46Z)
Annihilating Entanglement Between Cones [77.34726150561087]
We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
arXiv Detail & Related papers (2021-10-22T15:02:39Z)
Quantum double aspects of surface code models [77.34726150561087]
We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
arXiv Detail & Related papers (2021-06-25T17:03:38Z)
Anomalous Quantum Information Scrambling for $\mathbb{Z}_3$ Parafermion Chains [0.0]
Parafermions are exotic quasiparticles with non-Abelian fractional statistics. We study the scrambling of quantum information in one-dimensional parafermionic chains.
arXiv Detail & Related papers (2021-03-24T19:00:04Z)
Quantum information theory and Fourier multipliers on quantum groups [0.0]
We compute the exact values of the minimum output entropy and the completely bounded minimal entropy of quantum channels acting on matrix algebras. Our results use a new and precise description of bounded Fourier multipliers from $mathrmL1(mathbbG)$ into $mathrmLp(mathbbG)$ for $1 p leq infty$ where $mathbbG$ is a co-amenable locally compact quantum group.
arXiv Detail & Related papers (2020-08-27T09:47:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.