Grover's algorithm and the secant varieties

被引：14

作者：

Holweck, Frederic ^{[1
]}

Jaffali, Hamza ^{[1
]}

Nounouh, Ismael ^{[1
]}

机构：

[1] Univ Bourgogne Franche Comte, IRTES UTBM, F-90010 Belfort, France

来源：

QUANTUM INFORMATION PROCESSING | 2016年 / 15卷 / 11期

关键词：

Quantum algorithm; Entangled states; Secant varieties; SEARCH; ENTANGLEMENT;

D O I：

10.1007/s11128-016-1445-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper we investigate the entanglement nature of quantum states generated by Grover's search algorithm by means of algebraic geometry. More precisely we establish a link between entanglement of states generated by the algorithm and auxiliary algebraic varieties built from the set of separable states. This new perspective enables us to propose qualitative interpretations of earlier numerical results obtained by M. Rossi et al. We also illustrate our purpose with a couple of examples investigated in details.

引用

页码：4391 / 4413

页数：23

共 34 条

[1]

[Anonymous], 2011, QUANTUM COMPUTING GE, DOI DOI 10.1063/PT.3.1442

[2] Global versus local quantum correlations in the Grover search algorithm [J].

Batle, J. ;

Ooi, C. H. Raymond ;

Farouk, Ahmed ;

Alkhambashi, M. S. ;

Abdalla, S. .

QUANTUM INFORMATION PROCESSING, 2016, 15 (02) :833-849

[3] Exact and asymptotic measures of multipartite pure-state entanglement [J].

Bennett, Charles H., 2001, American Inst of Physics, Woodbury (63)

[4] Entanglement of three-qubit geometry [J].

Brody, Dorje C. ;

Gustavsson, Anna C. T. ;

Hughston, Lane P. .

THIRD INTERNATIONAL WORKSHOP DICE2006 - QUANTUM MECHANICS BETWEEN DECOHERENCE AND DETERMINISM: NEW ASPECTS FROM PARTICLE PHYSICS TO COSMOLOGY - CONTRIBUTED PAPERS, 2007, 67

[5]

Brylinski JL, 2002, COMP MATH SERIES, P3

[6]

Catalisano M.V., 2008, ARXIV08091701

[7]

Chakraborty S., 2013, ARXIV13054454

[8] Correlations in the Grover search [J].

Cui, Jian ;

Fan, Heng .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (04)

[9] Three qubits can be entangled in two inequivalent ways [J].

Dur, W. ;

Vidal, G. ;

Cirac, J.I. .

Physical Review A - Atomic, Molecular, and Optical Physics, 2000, 62 (06) :062314-062311

[10] Entanglement in the Grover search algorithm [J].

Fang, YY ;

Kaszlikowski, D ;

Chin, CM ;

Tay, K ;

Kwek, LC ;

Oh, CH .

PHYSICS LETTERS A, 2005, 345 (4-6) :265-272

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