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Computational Geometry Analysis of Quantum State Space and Its Applications.

Kimikazu Kato, Mayumi Oto, Hiroshi Imai +1 more

We show some coincidences of Voronoi diagrams in a quantum state space with respect to some distances. This means a computational geometry interpretation of a structure of a quantum state space. More properly, we investigate the Voronoi diagrams with respect to the divergence, Fubini-Study distance, Bures distance, geodesic distance and Euclidean distance.

Jan 1, 20080 citations

Geometry of the State Space of Quantum Mechanics

Pavel Bóna

Springer eBooksJan 1, 20200 citations

Algorithmic Quantum Entanglement Propagation for Computational Geometry

Jincheng Zhang

Quantum entanglement, a fundamental phenomenon in quantum mechanics, presents a unique pathway for manipulating information and creating complex correlations. This paper explores the algorithmic application of entanglement to propagate geometric information, aiming to facilitate the creation of intricate geometric structures and rigorous proofs of geometric theorems. The core mechanism centers around designing a "quantum map" – a state that utilizes entanglement to traverse geometric spaces, potentially enabling the generation of infinitely complex geometries. We present a novel algorithm that demonstrates the feasibility of this approach, highlighting its potential to revolutionize computational geometry and offer significant advancements in geometric analysis.Quantum entanglement, a fundamental phenomenon in quantum mechanics, presents a unique pathway for manipulating information and creating complex correlations. This paper explores the algorithmic application of entanglement to propagate geometric information, aiming to facilitate the creation of intricate geometric structures and rigorous proofs of geometric theorems. The core mechanism centers around designing a "quantum map" – a state that utilizes entanglement to traverse geometric spaces, potentially enabling the generation of infinitely complex geometries. We present a novel algorithm that demonstrates the feasibility of this approach, highlighting its potential to revolutionize computational geometry and offer significant advancements in geometric analysis.

Sep 6, 20260 citations

Geometry of Quantum Statesa

Samuel L. Braunstein, Carlton M. Caves

Annals of the New York Academy of SciencesApr 1, 19957 citations

量化信息论的动态空间结构分析

Jincheng Zhang

This paper investigates the application of quantum information theory to dynamic space structure analysis, aiming to automatically identify and analyze quantum entanglement or quantum information within a space. We propose a novel algorithm that leverages the inherent properties of quantum entanglement to model space geometry and predict future state evolutions. The core mechanism focuses on incorporating quantum state evolution as a key predictive tool. This work addresses the current limitations of existing quantum information theory applications by providing a framework for dynamically exploring and understanding spatial configurations. The paper details the algorithm's design, its potential benefits, and its approach to addressing challenges in quantum state analysis and space geometry.This paper investigates the application of quantum information theory to dynamic space structure analysis, aiming to automatically identify and analyze quantum entanglement or quantum information within a space. We propose a novel algorithm that leverages the inherent properties of quantum entanglement to model space geometry and predict future state evolutions. The core mechanism focuses on incorporating quantum state evolution as a key predictive tool. This work addresses the current limitations of existing quantum information theory applications by providing a framework for dynamically exploring and understanding spatial configurations. The paper details the algorithm's design, its potential benefits, and its approach to addressing challenges in quantum state analysis and space geometry.

Sep 7, 20260 citations

Geometry of quantum state space and quantum correlations

Prasenjit Deb

arXiv:1505.04682Quantum Information ProcessingJan 12, 201610 citations

Computational Geometry Analysis of Quantum State Space and Its Applications

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