Tensor rank problem in statistical high-dimensional data and quantum information theory:their comparisons on the methods and the results

2009/11/09 by Toshio Sakata, Lin Chen, Sakata, Toshio +5
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.48550/arxiv.0911.1663

6 pages, presented at "The 21st Quantum Information Technology Symposium (QIT21)", Chofugaoka Chofu-shi, Tokyo, Japan, November 4th, 2009

arxiv created 2009/11/09 · arxiv updated 2009/12/01

Abstract

Quantum communication is concerned with the complexity of entanglement of a state and statistical data analysis is concerned with the complexity of a model. A common key word for both is "rank". In this paper we will show that both community is tracing the same target and that the methods used are slightly different. Two different methods, the range criterion method from quantum communication and the determinant polynomial method, are shown as an examples.

Related

• The tensor as an informational resource
• Algebraic measures of entanglement
• Applications of Monotone Rank to Complexity Theory
• Cannikin's Law in Tensor Modeling: A Rank Study for Entanglement and Separability in Tensor Complexity and Model Capacity
• Separating quantum communication and approximate rank