A TENSOR VERSION OF THE QUANTUM WIELANDT THEOREM

Mateusz Michalek; Tim Seynnaeve; Frank Verstraete

doi:10.1137/18M1227664

A TENSOR VERSION OF THE QUANTUM WIELANDT THEOREM

Mateusz Michalek^*, Tim Seynnaeve, Frank Verstraete

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

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Abstract

We prove boundedness results for the injectivity regions for projected entangled pair states. Our result is a higher-dimensional generalization of the quantum Wielandt inequality.

Original language	English
Pages (from-to)	1125-1130
Number of pages	6
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	40
Issue number	3
DOIs	https://doi.org/10.1137/18M1227664
Publication status	Published - 2019
MoE publication type	A1 Journal article-refereed

Keywords

PEPS
quantum Wielandt
tensor
injectivity radius
nonlinear algebra

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10.1137/18M1227664

18m1227664Final published version, 309 KBLicence: CC BY

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title = "A TENSOR VERSION OF THE QUANTUM WIELANDT THEOREM",

abstract = "We prove boundedness results for the injectivity regions for projected entangled pair states. Our result is a higher-dimensional generalization of the quantum Wielandt inequality.",

keywords = "PEPS, quantum Wielandt, tensor, injectivity radius, nonlinear algebra",

author = "Mateusz Michalek and Tim Seynnaeve and Frank Verstraete",

year = "2019",

doi = "10.1137/18M1227664",

language = "English",

volume = "40",

pages = "1125--1130",

journal = "SIAM Journal on Matrix Analysis and Applications",

issn = "0895-4798",

publisher = "Society for Industrial and Applied Mathematics",

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T1 - A TENSOR VERSION OF THE QUANTUM WIELANDT THEOREM

AU - Michalek, Mateusz

AU - Seynnaeve, Tim

AU - Verstraete, Frank

PY - 2019

Y1 - 2019

N2 - We prove boundedness results for the injectivity regions for projected entangled pair states. Our result is a higher-dimensional generalization of the quantum Wielandt inequality.

AB - We prove boundedness results for the injectivity regions for projected entangled pair states. Our result is a higher-dimensional generalization of the quantum Wielandt inequality.

KW - PEPS

KW - quantum Wielandt

KW - tensor

KW - injectivity radius

KW - nonlinear algebra

U2 - 10.1137/18M1227664

DO - 10.1137/18M1227664

M3 - Article

SN - 0895-4798

VL - 40

SP - 1125

EP - 1130

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 3

ER -

A TENSOR VERSION OF THE QUANTUM WIELANDT THEOREM

Abstract

Keywords

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