A multigraph approach to confusability in quantum channels

• URL: http://arxiv.org/abs/2604.06072v1
• Date: Tue, 07 Apr 2026 16:52:24 GMT
• Title: A multigraph approach to confusability in quantum channels
• Abstract summary: We develop a theory of quantum multigraphs from Weaver's quantum relations point of view.<n>We provide a necessary and sufficient condition characterizing those quantum multigraphs that arise as quantum confusability multigraphs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. By``counting" the edges between two vertices of this confusability multigraph, one recovers the traditional confusability ``single-edged" graph of the channel. With this physical motivation, we therefore develop a theory of quantum multigraphs from Weaver's quantum relations point of view and explore its quantum graph theoretic properties. Finally, we provide a necessary and sufficient condition characterizing those quantum multigraphs that arise as quantum confusability multigraphs.

Related papers

• Quantum Port: Gamification of quantum teleportation for public engagement [0.0]
  We will refer to quantum theory as categorical quantum mechanics (CQM)<n>We propose the second level of transformation by gamifying the diagrammatic rules of quantum teleportation into a quantum card game called Quantum Port.
  arXiv  Detail & Related papers  (2025-03-17T09:39:10Z)
• Two-particle scattering on general graphs [0.0]
  Quantum walks in general graphs, or more specifically scattering on graphs, encompass enough complexity to perform universal quantum computation.<n>We start to develop a full theory of multi-particle scattering on graphs and give initial applications to build multi-particle gadgets with different properties.
  arXiv  Detail & Related papers  (2025-03-14T19:21:47Z)
• Entangled states from simple quantum graphs [0.0]
  Entanglement is a fundamental resource for many applications in quantum information processing.<n>We investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to generate entangled states.
  arXiv  Detail & Related papers  (2025-03-06T03:46:34Z)
• Two-Particle Scattering on Non-Translation Invariant Line Lattices [0.0]
  Quantum walks have been used to develop quantum algorithms since their inception. We show that a CPHASE gate can be achieved with high fidelity when the interaction acts only on a small portion of the line graph.
  arXiv  Detail & Related papers  (2023-03-08T02:36:29Z)
• Quantum symmetry in multigraphs (part I) [0.0]
  We introduce various notions of quantum symmetry in a directed or undirected multigraph. If the multigraph is single edged, all our notions of quantum symmetry reduce to already existing notions provided by Bichon and Banica.
  arXiv  Detail & Related papers  (2023-02-17T06:38:35Z)
• Lee-Yang theory of quantum phase transitions with neural network quantum states [0.0]
  We show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly-correlated spin lattices. Our results provide a starting point for determining the phase diagram of more complex quantum many-body systems.
  arXiv  Detail & Related papers  (2023-01-24T11:10:37Z)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• From Quantum Graph Computing to Quantum Graph Learning: A Survey [86.8206129053725]
  We first elaborate the correlations between quantum mechanics and graph theory to show that quantum computers are able to generate useful solutions. For its practicability and wide-applicability, we give a brief review of typical graph learning techniques. We give a snapshot of quantum graph learning where expectations serve as a catalyst for subsequent research.
  arXiv  Detail & Related papers  (2022-02-19T02:56:47Z)
• Entanglement catalysis for quantum states and noisy channels [41.94295877935867]
  We investigate properties of entanglement and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel.
  arXiv  Detail & Related papers  (2022-02-10T18:36:25Z)
• Holographic tensor network models and quantum error correction: A topical review [78.28647825246472]
  Recent progress in studies of holographic dualities has led to a confluence with concepts and techniques from quantum information theory. A particularly successful approach has involved capturing holographic properties by means of tensor networks.
  arXiv  Detail & Related papers  (2021-02-04T14:09:21Z)
• Quantum information spreading in a disordered quantum walk [50.591267188664666]
  We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
  arXiv  Detail & Related papers  (2020-10-20T20:03:19Z)
• Exploring complex graphs using three-dimensional quantum walks of correlated photons [52.77024349608834]
  We introduce a new paradigm for the direct experimental realization of excitation dynamics associated with three-dimensional networks. This novel testbed for the experimental exploration of multi-particle quantum walks on complex, highly connected graphs paves the way towards exploiting the applicative potential of fermionic dynamics in integrated quantum photonics.
  arXiv  Detail & Related papers  (2020-07-10T09:15:44Z)
• Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs [62.997667081978825]
  We study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer. The essential goal is to develop the theoretical framework for understanding the interplay between perfect quantum state transfer, spectral properties, and the geometry of the underlying graph.
  arXiv  Detail & Related papers  (2020-03-25T02:46:14Z)

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.