Related papers: Geometry of generalized Pauli channels

Geometry of generalized Pauli channels

URL: http://arxiv.org/abs/2002.04657v2
Date: Wed, 15 Apr 2020 21:48:17 GMT
Title: Geometry of generalized Pauli channels
Authors: Katarzyna Siudzi\'nska
Abstract summary: Choi-Jamiolkowski isomorphism allows us to express the Hilbert-Schmidt line and volume elements in terms of the eigenvalues of the generalized Pauli maps. We analytically compute the volume of generalized Pauli channels and their important subclasses.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We analyze the geometry of the generalized Pauli channels constructed from the mutually unbiased bases. The Choi-Jamio{\l}kowski isomorphism allows us to express the Hilbert-Schmidt line and volume elements in terms of the eigenvalues of the generalized Pauli maps. After determining appropriate regions of integration, we analytically compute the volume of generalized Pauli channels and their important subclasses. In particular, we obtain the volumes of the generalized Pauli channels that can be generated by a legitimate generator and are entanglement breaking. We also provide the upper bound for the volume of positive, trace-preserving generalized Pauli maps.

Related papers

Full classification of Pauli Lie algebras [0.29998889086656577]
We provide a comprehensive classification of Lie algebras generated by an arbitrary set of Pauli operators. We find a no-go result for the existence of small Lie algebras beyond the free-fermionic case in the Pauli setting. These results bear significant impact in ideas in a number of fields like quantum control, quantum machine learning, or classical simulation of quantum circuits.
arXiv Detail & Related papers (2024-07-31T18:00:11Z)
Non-Markovian quantum dynamics from symmetric measurements [0.0]
We use symmetric measurement operators to construct quantum channels that provide a further generalization of generalized Pauli channels. We analyze their important properties, such as complete positivity and the ability to break quantum entanglement.
arXiv Detail & Related papers (2024-02-06T21:26:22Z)
Beyond the mixture of generalized Pauli dephasing channels [3.4521402245831583]
We show that non-invertibility of mixed channels is not a prerequisite for the resulting mapping to constitute a Markovian semigroup. We demonstrate that every Pauli channel can be represented as a mixture of $(d+1)$ Pauli dephasing channels, but this generalization doesn't apply to higher dimensions.
arXiv Detail & Related papers (2023-09-10T00:50:38Z)
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)
Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
arXiv Detail & Related papers (2020-11-06T19:00:07Z)
Scaling limits of lattice quantum fields by wavelets [62.997667081978825]
The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field.
arXiv Detail & Related papers (2020-10-21T16:30:06Z)
Geometry of symmetric and non-invertible Pauli channels [0.0]
We analyze positive and completely positive, trace preserving Pauli maps that are fully determined by up to two distinct parameters. Using the Hilbert-Schmidt metric in the space of the Choi-Jamiolkowski states, we compute the relative volumes of entanglement breaking, time-local generated, and divisible channels.
arXiv Detail & Related papers (2020-10-02T17:52:37Z)
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)
Generalization of Pauli channels through mutually unbiased measurements [0.0]
We introduce a new generalization of the Pauli channels using the mutually unbiased measurement operators. We analyze the channel properties, such as complete positivity, entanglement breaking, and multiplicativity of maximal output purity.
arXiv Detail & Related papers (2020-03-26T22:27:56Z)
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)
A refinement of Reznick's Positivstellensatz with applications to quantum information theory [72.8349503901712]
In Hilbert's 17th problem Artin showed that any positive definite in several variables can be written as the quotient of two sums of squares. Reznick showed that the denominator in Artin's result can always be chosen as an $N$-th power of the squared norm of the variables.
arXiv Detail & Related papers (2019-09-04T11:46:26Z)

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