The tensor rank of tensor product of two three-qubit W states is eight

被引：30

作者：

Chen, Lin ^{[1
,2
]}

Friedland, Shmuel ^{[3
]}

机构：

[1] Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China

[2] Beihang Univ, Int Res Inst Multidisciplinary Sci, Beijing 100191, Peoples R China

[3] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2018年 / 543卷

基金：

北京市自然科学基金;

关键词：

Tensor rank; Qubit; W state; Kronecker product; Tensor product;

D O I：

10.1016/j.laa.2017.12.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A.K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：1 / 16

页数：16

共 50 条

[41] Invariants for a class of nongeneric three-qubit states
Sun Bao-Zhi
Fei Shao-Ming
COMMUNICATIONS IN THEORETICAL PHYSICS, 2006, 45 (06) : 1007 - 1010
[42] Entanglement of Three-Qubit Random Pure States
Enriquez, Marco
Delgado, Francisco
Zyczkowski, Karol
ENTROPY, 2018, 20 (10):
[43] Separability criteria for mixed three-qubit states
Szalay, Szilard
PHYSICAL REVIEW A, 2011, 83 (06):
[44] Disentanglement of three-qubit states in a noisy environment
Huang, Jie-Hui
Wang, Li-Gang
Zhu, Shi-Yao
PHYSICAL REVIEW A, 2010, 81 (06):
[45] Two-way and three-way negativities of three-qubit entangled states
Sharma, S. Shelly
Sharma, N. K.
PHYSICAL REVIEW A, 2007, 76 (01):
[46] Two-qubit and three-qubit geometry and Hopf fibrations
Mosseri, R
TOPOLOGY IN CONDENSED MATTER, 2006, 150 : 187 - 203
[47] Tensor-product representation of qubits and tensor realization of one-qubit operators
Adam, Peter
Andreev, Vladimir A.
Janszky, Jozsef
Man'ko, Margarita A.
Man'ko, Vladimir I.
PHYSICA SCRIPTA, 2013, T153
[48] Perfect Teleportation of an Arbitrary Three-Qubit State by Using W-Class States
Yi-you Nie
Yuan-hua Li
Jun-chang Liu
Ming-huang Sang
International Journal of Theoretical Physics, 2011, 50
[49] Eigenvalue-based quantum state verification of three-qubit W class states
Bao, Daipengwei
Liu, Min
Ou, Yangwei
Xu, Qingshan
Li, Qin
Tan, Xiaoqing
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2024, 639
[50] Perfect Teleportation of an Arbitrary Three-Qubit State by Using W-Class States
Nie, Yi-you
Li, Yuan-hua
Liu, Jun-chang
Sang, Ming-huang
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2011, 50 (10) : 3225 - 3229

← 1 2 3 4 5 →