Constructing 2 × 2 × 4 and 4 × 4 unextendible product bases and positive-partial-transpose entangled states

Kai Wang; Lin Chen; Yi Shen; Yize Sun; Li Jun Zhao

doi:10.1080/03081087.2019.1588849

Constructing 2 × 2 × 4 and 4 × 4 unextendible product bases and positive-partial-transpose entangled states

Kai Wang
, Lin Chen^*
, Yi Shen
, Yize Sun
, Li Jun Zhao

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

8 Scopus citations

Abstract

The 4-qubit unextendible product bases (UPBs) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. Based on this study we show that there is only one UPB of size 6 and six UPBs of size 9 in (Formula presented.), three UPBs of size 9 in (Formula presented.), and no UPB of size 7 in (Formula presented.) and (Formula presented.). Furthermore we construct a new family of 4-qubit positive-partial-transpose (PPT) entangled states of rank seven, and show that they are also PPT entangled states in (Formula presented.) and (Formula presented.), respectively. We analytically derive a geometric measure of a special PPT entangled states.

Original language	English
Pages (from-to)	131-146
Number of pages	16
Journal	Linear and Multilinear Algebra
Volume	69
Issue number	1
DOIs	https://doi.org/10.1080/03081087.2019.1588849
State	Published - 2021

Keywords

03.65.Ud
03.67.Mn
Unextendible product basis (UPB)
entanglement
four qubit system
positive partial transpose (PPT)

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10.1080/03081087.2019.1588849

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title = "Constructing 2 × 2 × 4 and 4 × 4 unextendible product bases and positive-partial-transpose entangled states",

abstract = "The 4-qubit unextendible product bases (UPBs) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. Based on this study we show that there is only one UPB of size 6 and six UPBs of size 9 in (Formula presented.), three UPBs of size 9 in (Formula presented.), and no UPB of size 7 in (Formula presented.) and (Formula presented.). Furthermore we construct a new family of 4-qubit positive-partial-transpose (PPT) entangled states of rank seven, and show that they are also PPT entangled states in (Formula presented.) and (Formula presented.), respectively. We analytically derive a geometric measure of a special PPT entangled states.",

keywords = "03.65.Ud, 03.67.Mn, Unextendible product basis (UPB), entanglement, four qubit system, positive partial transpose (PPT)",

author = "Kai Wang and Lin Chen and Yi Shen and Yize Sun and Zhao, \{Li Jun\}",

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year = "2021",

doi = "10.1080/03081087.2019.1588849",

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TY - JOUR

T1 - Constructing 2 × 2 × 4 and 4 × 4 unextendible product bases and positive-partial-transpose entangled states

AU - Wang, Kai

AU - Chen, Lin

AU - Shen, Yi

AU - Sun, Yize

AU - Zhao, Li Jun

PY - 2021

Y1 - 2021

N2 - The 4-qubit unextendible product bases (UPBs) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. Based on this study we show that there is only one UPB of size 6 and six UPBs of size 9 in (Formula presented.), three UPBs of size 9 in (Formula presented.), and no UPB of size 7 in (Formula presented.) and (Formula presented.). Furthermore we construct a new family of 4-qubit positive-partial-transpose (PPT) entangled states of rank seven, and show that they are also PPT entangled states in (Formula presented.) and (Formula presented.), respectively. We analytically derive a geometric measure of a special PPT entangled states.

AB - The 4-qubit unextendible product bases (UPBs) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. Based on this study we show that there is only one UPB of size 6 and six UPBs of size 9 in (Formula presented.), three UPBs of size 9 in (Formula presented.), and no UPB of size 7 in (Formula presented.) and (Formula presented.). Furthermore we construct a new family of 4-qubit positive-partial-transpose (PPT) entangled states of rank seven, and show that they are also PPT entangled states in (Formula presented.) and (Formula presented.), respectively. We analytically derive a geometric measure of a special PPT entangled states.

KW - 03.65.Ud

KW - 03.67.Mn

KW - Unextendible product basis (UPB)

KW - entanglement

KW - four qubit system

KW - positive partial transpose (PPT)

UR - https://www.scopus.com/pages/publications/85062984210

U2 - 10.1080/03081087.2019.1588849

DO - 10.1080/03081087.2019.1588849

M3 - 文章

AN - SCOPUS:85062984210

SN - 0308-1087

VL - 69

SP - 131

EP - 146

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 1

ER -

Constructing 2 × 2 × 4 and 4 × 4 unextendible product bases and positive-partial-transpose entangled states

Abstract

Keywords

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