Iterations of nonlinear entanglement witnesses

被引：18

作者：

Moroder, Tobias ^{[1
,2
,3
]}

Guehne, Otfried ^{[4
,5
]}

Luetkenhaus, Norbert ^{[1
,2
,3
]}

机构：

[1] Univ Erlangen Nurnberg, Quantum Informat Theory Grp, Inst Theoret Phys 1, D-91058 Erlangen, Germany

[2] Univ Erlangen Nurnberg, Max Planck Res Grp Opt Photon & Informat, D-91058 Erlangen, Germany

[3] Univ Waterloo, Inst Quantum Comp, Waterloo, ON N2L 3G1, Canada

[4] Austrian Acad Sci, Inst Quantenopt & Quanteninformat, Innsbruck, Austria

[5] Univ Innsbruck, Inst Theoret Phys, A-6020 Innsbruck, Austria

来源：

PHYSICAL REVIEW A | 2008年 / 78卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

D O I：

10.1103/PhysRevA.78.032326

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We describe a generic way to improve a given linear entanglement witness by a quadratic, nonlinear term. This method can be iterated, leading to a whole sequence of nonlinear witnesses, which become stronger in each step of the iteration. We show how to optimize this iteration with respect to a given state and prove that in the limit of the iteration the nonlinear witness detects all states that can be detected by the positive map corresponding to the original linear witness.

引用

页数：10

共 40 条

[1]

[Anonymous], 1995, MATRIX ANAL

[2] Experimental detection of multipartite entanglement using witness operators -: art. no. 087902 [J].

Bourennane, M ;

Eibl, M ;

Kurtsiefer, C ;

Gaertner, S ;

Weinfurter, H ;

Gühne, O ;

Hyllus, P ;

Bruss, D ;

Lewenstein, M ;

Sanpera, A .

PHYSICAL REVIEW LETTERS, 2004, 92 (08)

[3] Characterization of the positivity of the density matrix in terms of the coherence vector representation [J].

Byrd, MS ;

Khaneja, N .

PHYSICAL REVIEW A, 2003, 68 (06) :13

[4] Noiseless quantum circuits for the Peres separability criterion [J].

Carteret, HA .

PHYSICAL REVIEW LETTERS, 2005, 94 (04)

[5]

Chen K, 2003, QUANTUM INF COMPUT, V3, P193

[6] COMPLETELY POSITIVE LINEAR MAPS ON COMPLEX MATRICES [J].

CHOI, MD .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1975, 10 (03) :285-290

[7]

CHOI MD, 1982, P SYMP PURE MATH, V38, P583

[8] LINEAR TRANSFORMATIONS WHICH PRESERVE HERMITIAN AND POSITIVE SEMIDEFINITE OPERATORS [J].

DEPILLIS, J .

PACIFIC JOURNAL OF MATHEMATICS, 1967, 23 (01) :129-&

[9] Complete family of separability criteria [J].

Doherty, AC ;

Parrilo, PA ;

Spedalieri, FM .

PHYSICAL REVIEW A, 2004, 69 (02) :20

[10] Complete hierarchies of efficient approximations to problems in entanglement theory -: art. no. 062317 [J].

Eisert, J ;

Hyllus, P ;

Gühne, O ;

Curty, M .

PHYSICAL REVIEW A, 2004, 70 (06) :062317-1

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