Optimal entanglement witnesses for qubits and qutrits

被引:61
作者
Bertlmann, RA [1 ]
Durstberger, K [1 ]
Hiesmayr, BC [1 ]
Krammer, P [1 ]
机构
[1] Univ Vienna, Inst Theoret Phys, A-1090 Vienna, Austria
来源
PHYSICAL REVIEW A | 2005年 / 72卷 / 05期
关键词
D O I
10.1103/PhysRevA.72.052331
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We study the connection between the Hilbert-Schmidt measure of entanglement (that is the minimal distance of an entangled state to the set of separable states) and entanglement witness in terms of a generalized Bell inequality which distinguishes between entangled and separable states. A method for checking the nearest separable state to a given entangled one is presented. We illustrate the general results by considering isotropic states, in particular two-qubit and two-qutrit states-and their generalizations to arbitrary dimensions-where we calculate the optimal entanglement witnesses explicitly.
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页数:9
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共 35 条
[11]   Can quantum-mechanical description of physical reality be considered complete? [J].
Einstein, A ;
Podolsky, B ;
Rosen, N .
PHYSICAL REVIEW, 1935, 47 (10) :0777-0780
[12]   Experimental detection of entanglement via witness operators and local measurements [J].
Gühne, O ;
Hyllus, P ;
Bruss, D ;
Ekert, A ;
Lewenstein, M ;
Macchiavello, C ;
Sanpera, A .
JOURNAL OF MODERN OPTICS, 2003, 50 (6-7) :1079-1102
[13]  
Henley E. M., 1962, Elementary Quantum Field Theory
[14]   Entanglement of a pair of quantum bits [J].
Hill, S ;
Wootters, WK .
PHYSICAL REVIEW LETTERS, 1997, 78 (26) :5022-5025
[15]   Separability of mixed states: Necessary and sufficient conditions [J].
Horodecki, M ;
Horodecki, P ;
Horodecki, R .
PHYSICS LETTERS A, 1996, 223 (1-2) :1-8
[16]  
Horodecki M, 2001, SPRINGER TR MOD PHYS, V173, P151
[17]   Reduction criterion of separability and limits for a class of distillation protocols [J].
Horodecki, M ;
Horodecki, P .
PHYSICAL REVIEW A, 1999, 59 (06) :4206-4216
[18]   Improved algorithm for quantum separability and entanglement detection [J].
Ioannou, LM ;
Travaglione, BC ;
Cheung, D ;
Ekert, AK .
PHYSICAL REVIEW A, 2004, 70 (06) :060303-1
[19]   Optimization of entanglement witnesses [J].
Lewenstein, M ;
Kraus, B ;
Cirac, JI ;
Horodecki, P .
PHYSICAL REVIEW A, 2000, 62 (05) :052310-052311
[20]   Entanglement measures and the Hilbert-Schmidt distance [J].
Ozawa, M .
PHYSICS LETTERS A, 2000, 268 (03) :158-160