Related papers: Entanglement-symmetries of covariant channels

Entanglement-symmetries of covariant channels

URL: http://arxiv.org/abs/2012.05761v8
Date: Thu, 15 Feb 2024 16:43:55 GMT
Title: Entanglement-symmetries of covariant channels
Authors: Dominic Verdon
Abstract summary: We show that, if the Hopf-Galois object H has a finite-dimensional *-representation, then channels related by this equivalence can simulate each other. We use this result to calculate the entanglement-assisted capacities of certain quantum channels.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Let G and G' be monoidally equivalent compact quantum groups, and let H be a Hopf-Galois object realising a monoidal equivalence between these groups' representation categories. This monoidal equivalence induces an equivalence Chan(G) -> Chan(G'), where Chan(G) is the category whose objects are finite-dimensional C*-algebras with an action of G and whose morphisms are covariant channels. We show that, if the Hopf-Galois object H has a finite-dimensional *-representation, then channels related by this equivalence can simulate each other using a finite-dimensional entangled resource. We use this result to calculate the entanglement-assisted capacities of certain quantum channels.

Related papers

Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
arXiv Detail & Related papers (2024-08-19T09:15:54Z)
Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
arXiv Detail & Related papers (2024-06-15T17:39:32Z)
Geometric Quantum Machine Learning with Horizontal Quantum Gates [41.912613724593875]
We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions to those of the symmetry. For a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem.
arXiv Detail & Related papers (2024-06-06T18:04:39Z)
A Universal Kinematical Group for Quantum Mechanics [0.0]
In 1968, Dashen and Sharp obtained a certain singular Lie algebra of local densities and currents from canonical commutation relations in nonrelativistic quantum field theory. The corresponding Lie group is infinite dimensional: the natural semidirect product of an additive group of scalar functions with a group of diffeomorphisms.
arXiv Detail & Related papers (2024-04-28T18:46:24Z)
Enriching Diagrams with Algebraic Operations [49.1574468325115]
We extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We show how this construction can be used for diagrammatic reasoning of noise in quantum systems.
arXiv Detail & Related papers (2023-10-17T14:12:39Z)
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)
Coherence generation, symmetry algebras and Hilbert space fragmentation [0.0]
We show a simple connection between classification of physical systems and their coherence generation properties, quantified by the coherence generating power (CGP) We numerically simulate paradigmatic models with both ordinary symmetries and Hilbert space fragmentation, comparing the behavior of the CGP in each case with the system dimension.
arXiv Detail & Related papers (2022-12-29T18:31:16Z)
On quantum channels generated by covariant positive operator-valued measures on a locally compact group [0.0]
We introduce positive operator-valued measure (POVM) generated by the projective unitary representation of a direct product of locally compact Abelian group $G$ with its dual $hat G$. The method is based upon the Pontryagin duality allowing to establish an isometrical isomorphism between the space of Hilbert-Schmidt operators in $L2(G)$ and the Hilbert space $L2(hat Gtimes G)$.
arXiv Detail & Related papers (2022-09-08T10:42:01Z)
A covariant Stinespring theorem [0.0]
We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. We show that finite-dimensional G-C*-algebras can be identified with equivalence classes of 1-morphisms out of the object T in Mod(T)
arXiv Detail & Related papers (2021-08-23T00:20:04Z)
Particle on the sphere: group-theoretic quantization in the presence of a magnetic monopole [0.0]
We consider the problem of quantizing a particle on a 2-sphere. We construct the Hilbert space directly from the symmetry algebra. We show how the Casimir invariants of the algebra determine the bundle topology.
arXiv Detail & Related papers (2020-11-10T04:42:08Z)
Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
arXiv Detail & Related papers (2020-01-16T17:44:52Z)

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