State Transfer and Readout Times for Trees of Diameter 4
- URL: http://arxiv.org/abs/2406.15289v1
- Date: Fri, 21 Jun 2024 16:32:45 GMT
- Title: State Transfer and Readout Times for Trees of Diameter 4
- Authors: Stephen Kirkland, Christopher M. van Bommel,
- Abstract summary: We consider the state transfer properties of continuous time quantum walks on trees of diameter 4.
For each type, we construct an infinite family of diameter 4 trees for which there is pretty good state transfer.
For strongly cospectral vertices of the remaining type, we identify a sequence of trees and explicit readout times.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider the state transfer properties of continuous time quantum walks on trees of diameter 4. We characterize all pairs of strongly cospectral vertices in trees of diameter 4, finding that they fall into pairs of three different types. For each type, we construct an infinite family of diameter 4 trees for which there is pretty good state transfer between the pair of strongly cospectral vertices. Moreover, for two of those types, for each tree in the infinite family, we give an explicit sequence of readout times at which the fidelity of state transfer converges to $1$. For strongly cospectral vertices of the remaining type, we identify a sequence of trees and explicit readout times so that the fidelity of state transfer between the strongly cospectral vertices approaches $1.$ We also prove a result of independent interest: for a graph with the property that the fidelity of state transfer between a pair of vertices at time $t_k$ converges to $1$ as $k \rightarrow \infty,$ then the derivative of the fidelity at $t_k$ converges to $0$ as $k \rightarrow \infty. $
Related papers
- A generalization of quantum pair state transfer [0.0]
An $s$-pair state in a graph is a quantum state of the form $mathbfe_u+smathbfe_v$.
We develop the theory of perfect $s$-pair state transfer in continuous quantum walks.
arXiv Detail & Related papers (2024-04-25T14:45:49Z) - Almost zero transfer in continuous-time quantum walks on weighted tree graphs [0.0]
We study continuous-time quantum walks on weighted tree graphs.
We map Cayley trees $C_3,2$ and $C_3,3$ into these spider graphs and observe the same dependency.
arXiv Detail & Related papers (2024-04-05T13:41:11Z) - Entanglement and Bell inequalities violation in $H\to ZZ$ with anomalous coupling [44.99833362998488]
We discuss entanglement and violation of Bell-type inequalities for a system of two $Z$ bosons produced in Higgs decays.
We find that a $ZZ$ state is entangled and violates the inequality for all values of the pair (anomalous) coupling constant.
arXiv Detail & Related papers (2023-07-25T13:44:31Z) - Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
arXiv Detail & Related papers (2023-06-21T10:11:28Z) - Beyond the Berry Phase: Extrinsic Geometry of Quantum States [77.34726150561087]
We show how all properties of a quantum manifold of states are fully described by a gauge-invariant Bargmann.
We show how our results have immediate applications to the modern theory of polarization.
arXiv Detail & Related papers (2022-05-30T18:01:34Z) - Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping [45.873301228345696]
localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) propto r-2$ is not resolved yet.
We show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions there exist two distinguishable phases at weak and strong disorder.
arXiv Detail & Related papers (2022-05-29T16:53:20Z) - $n$-qubit states with maximum entanglement across all bipartitions: A
graph state approach [0.0]
We show that a subset of the 'graph states' satisfy this condition, hence providing a recipe for constructing $k$-uniform states.
Finding recipes for construction of $k$-uniform states using graph states is useful since every graph state can be constructed starting from a product state.
arXiv Detail & Related papers (2022-01-14T19:00:09Z) - State Transfer on Paths with Weighted Loops [0.0]
It is known that if $w$ is transcendental, then there is pretty good state transfer from one end to the other.
We prove a companion result to that fact, namely that there is a dense subset of $[1,infty)$ such that if $w$ is in that subset, pretty good state transfer between end vertices is impossible.
arXiv Detail & Related papers (2021-12-04T16:11:40Z) - Laplacian State Transfer on Graphs with an Edge Perturbation Between
Twin Vertices [0.0]
We consider quantum state transfer relative to the Laplacian matrix of a graph.
We investigate the existence of quantum state transfer between a pair of twin vertices in a graph when the edge between the vertices is perturbed.
arXiv Detail & Related papers (2021-09-11T15:48:18Z) - Stochastic behavior of outcome of Schur-Weyl duality measurement [45.41082277680607]
We focus on the measurement defined by the decomposition based on Schur-Weyl duality on $n$ qubits.
We derive various types of distribution including a kind of central limit when $n$ goes to infinity.
arXiv Detail & Related papers (2021-04-26T15:03:08Z) - Scattering data and bound states of a squeezed double-layer structure [77.34726150561087]
A structure composed of two parallel homogeneous layers is studied in the limit as their widths $l_j$ and $l_j$, and the distance between them $r$ shrinks to zero simultaneously.
The existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function.
The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
arXiv Detail & Related papers (2020-11-23T14:40:27Z)
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.