Interpolating between Positive and Completely Positive Maps: A New Hierarchy of Entangled States

被引:2
作者
Siudzinska, Katarzyna [1 ]
Chakraborty, Sagnik [1 ]
Chruscinski, Dariusz [1 ]
机构
[1] Nicolaus Copernicus Univ, Inst Phys, Fac Phys Astron & Informat, Ul Grudziadzka 5-7, PL-87100 Torun, Poland
关键词
qubit maps; contractivity; Schwarz inequality; positive maps; Schmidt number; SCHMIDT NUMBER; LINEAR MAPS; MATRICES;
D O I
10.3390/e23050625
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A new class of positive maps is introduced. It interpolates between positive and completely positive maps. It is shown that this class gives rise to a new characterization of entangled states. Additionally, it provides a refinement of the well-known classes of entangled states characterized in terms of the Schmidt number. The analysis is illustrated with examples of qubit maps.
引用
收藏
页数:10
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共 35 条
  • [11] On Kadison-Schwarz Approximation to Positive Maps
    Chruscinski, Dariusz
    Mukhamedov, Farrukh
    Hajji, Mohamed Ali
    [J]. OPEN SYSTEMS & INFORMATION DYNAMICS, 2020, 27 (03)
  • [12] Entanglement witnesses: construction, analysis and classification
    Chruscinski, Dariusz
    Sarbicki, Gniewomir
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (48)
  • [13] Spectral Conditions for Positive Maps
    Chruscinski, Dariusz
    Kossakowski, Andrzej
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 290 (03) : 1051 - 1064
  • [14] Extension of the Alberti-Ulhmann criterion beyond qubit dichotomies
    Dall'Arno, Michele
    Buscemi, Francesco
    Scarani, Valerio
    [J]. QUANTUM, 2020, 4
  • [15] Schmidt measure as a tool for quantifying multiparticle entanglement
    Eisert, Jens
    Briegel, Hans J.
    [J]. Physical Review A. Atomic, Molecular, and Optical Physics, 2001, 64 (02): : 1 - 022306
  • [16] POSITIVE DEFINITE MATRICES AND SYLVESTER CRITERION
    GILBERT, GT
    [J]. AMERICAN MATHEMATICAL MONTHLY, 1991, 98 (01) : 44 - 46
  • [17] Entanglement detection
    Guehne, Otfried
    Toth, Geza
    [J]. PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2009, 474 (1-6): : 1 - 75
  • [18] A generalization of Schmidt number for multipartite states
    Guo, Yu
    Fan, Heng
    [J]. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2015, 13 (03)
  • [19] Hayashi M., 2006, Quantum Information: An Introduction
  • [20] Extending quantum operations
    Heinosaari, Teiko
    Jivulescu, Maria A.
    Reeb, David
    Wolf, Michael M.
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (10)