Self-Testing of Symmetric Three-Qubit States

被引：6

作者：

Li, Xinhui ^{[1
,2
]}

Wang, Yukun ^{[3
]}

Han, Yunguang ^{[4
,5
,6
]}

Qin, Sujuan ^{[1
]}

Gao, Fei ^{[1
,7
]}

Wen, Qiaoyan ^{[1
]}

机构：

[1] Beijing Univ Posts & Telecommun, State Key Lab Networking & Switching Technol, Beijing 100876, Peoples R China

[2] State Key Lab Cryptol, Beijing 100878, Peoples R China

[3] Natl Univ Singapore, Dept Elect & Comp Engn, Singapore 117543, Singapore

[4] Fudan Univ, Dept Phys, Shanghai 200433, Peoples R China

[5] Fudan Univ, Ctr Field Theory & Particle Phys, Shanghai 200433, Peoples R China

[6] Fudan Univ, State Key Lab Surface Phys, Shanghai 200433, Peoples R China

[7] Peng Cheng Lab, Ctr Quantum Comp, Shenzhen 518055, Guangdong, Peoples R China

来源：

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS | 2020年 / 38卷 / 03期

关键词：

Entanglement; symmetric states; self-testing; Bell inequality; QUANTUM COMMUNICATION;

D O I：

10.1109/JSAC.2020.2968994

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

Self-testing refers to a device-independent way to uniquely identify an unknown quantum device based only on the observed statistics. Earlier results on self-testing of multipartite state were restricted either to Dicke states or Graph states. In this paper, we propose self-testing schemes for a large family of symmetric three-qubit states, namely the superposition of $W$ state and $GHZ$ state. We first propose and analytically prove a self-testing criterion for the special symmetric state with equal coefficients of the canonical bases, by designing subsystem self-testing of partially and maximally entangled state simultaneously. Then we demonstrate for the general case, the states can be self-tested numerically by the swap method combining semidefinite programming (SDP) in high precision.

引用

页码：589 / 597

页数：9

共 37 条

[1] Generalized Schmidt decomposition and classification of three-quantum-bit states [J].

Acín, A ;

Andrianov, A ;

Costa, L ;

Jané, E ;

Latorre, JI ;

Tarrach, R .

PHYSICAL REVIEW LETTERS, 2000, 85 (07) :1560-1563

[2] Three-qubit pure-state canonical forms [J].

Acín, A ;

Andrianov, A ;

Jané, E ;

Tarrach, R .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (35) :6725-6739

[3] Device-independent security of quantum cryptography against collective attacks [J].

Acin, Antonio ;

Brunner, Nicolas ;

Gisin, Nicolas ;

Massar, Serge ;

Pironio, Stefano ;

Scarani, Valerio .

PHYSICAL REVIEW LETTERS, 2007, 98 (23)

[4] Sum-of-squares decompositions for a family of Clauser-Horne-Shimony-Holt-like inequalities and their application to self-testing [J].

Bamps, Cedric ;

Pironio, Stefano .

PHYSICAL REVIEW A, 2015, 91 (05)

[5] Physical characterization of quantum devices from nonlocal correlations [J].

Bancal, Jean-Daniel ;

Navascues, Miguel ;

Scarani, Valerio ;

Vertesi, Tamas ;

Yang, Tzyh Haur .

PHYSICAL REVIEW A, 2015, 91 (02)

[6] TELEPORTING AN UNKNOWN QUANTUM STATE VIA DUAL CLASSICAL AND EINSTEIN-PODOLSKY-ROSEN CHANNELS [J].

BENNETT, CH ;

BRASSARD, G ;

CREPEAU, C ;

JOZSA, R ;

PERES, A ;

WOOTTERS, WK .

PHYSICAL REVIEW LETTERS, 1993, 70 (13) :1895-1899

[7] Public Quantum Communication and Superactivation [J].

Brandao, Fernando G. S. L. ;

Oppenheim, Jonathan .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (04) :2517-2526

[8] Testing the Structure of Multipartite Entanglement with Bell Inequalities [J].

Brunner, Nicolas ;

Sharam, James ;

Vertesi, Tamas .

PHYSICAL REVIEW LETTERS, 2012, 108 (11)

[9] PROPOSED EXPERIMENT TO TEST LOCAL HIDDEN-VARIABLE THEORIES [J].

CLAUSER, JF ;

HORNE, MA ;

SHIMONY, A ;

HOLT, RA .

PHYSICAL REVIEW LETTERS, 1969, 23 (15) :880-&

[10] All pure bipartite entangled states can be self-tested [J].

Coladangelo, Andrea ;

Goh, Koon Tong ;

Scarani, Valerio .

NATURE COMMUNICATIONS, 2017, 8

← 1 2 3 4 →