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

[21] Measuring the Tangle of Three-Qubit States
Perez-Salinas, Adrian
Garcia-Martin, Diego
Bravo-Prieto, Carlos
Latorre, Jose, I
ENTROPY, 2020, 22 (04)
[22] Bisplitting an Arbitrary N-Qubit State with a Class of Asymmetric Three-Qubit W States
Xue-qin Zuo
Yi-min Liu
Zi-yun Zhang
Zhan-jun Zhang
International Journal of Theoretical Physics, 2009, 48 : 1950 - 1956
[23] Tripartite quantum operation sharing with two asymmetric three-qubit W states in five entanglement structures
Qibin Ji
Yimin Liu
Chuanmei Xie
Xiaofeng Yin
Zhanjun Zhang
Quantum Information Processing, 2014, 13 : 1659 - 1676
[24] Tomographic characterization of three-qubit pure states with only two-qubit detectors
Cavalcanti, D
Cioletti, LM
Cunha, MOT
PHYSICAL REVIEW A, 2005, 71 (01):
[25] CATEGORICAL W]-TENSOR PRODUCT
DAUNS, J
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (02): : A317 - A317
[26] Tripartite quantum operation sharing with two asymmetric three-qubit W states in five entanglement structures
Ji, Qibin
Liu, Yimin
Xie, Chuanmei
Yin, Xiaofeng
Zhang, Zhanjun
QUANTUM INFORMATION PROCESSING, 2014, 13 (08) : 1659 - 1676
[27] TENSOR PRODUCT OF W ALGEBRAS
RENSHAW, BB
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 194 (JUL) : 337 - 347
[28] CATEGORICAL W]-TENSOR PRODUCT
DAUNS, J
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 166 (NAPR) : 439 - &
[29] MAXIMAL RANK OF AN ELEMENT OF A TENSOR PRODUCT
BAILEY, RA
ROWLEY, CA
LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 182 : 1 - 7
[30] ON TENSOR PRODUCT OF W'-ALGEBRAS
SAKAI, S
AMERICAN JOURNAL OF MATHEMATICS, 1968, 90 (02) : 335 - &

← 1 2 3 4 5 →