-
1
-
-
33947385649
-
-
PHRVAO 0031-899X 10.1103/PhysRev.47.777
-
A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.47.777 47, 777 (1935).
-
(1935)
Phys. Rev.
, vol.47
, pp. 777
-
-
Einstein, A.1
Podolsky, B.2
Rosen, N.3
-
2
-
-
11744373290
-
-
NATWAY 0028-1042 10.1007/BF01491891
-
E. Schrödinger, Naturwiss. NATWAY 0028-1042 10.1007/BF01491891 23, 807 (1935).
-
(1935)
Naturwiss.
, vol.23
, pp. 807
-
-
Schrödinger, E.1
-
3
-
-
0039624459
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.40.4277
-
R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
-
(1989)
Phys. Rev. A
, vol.40
, pp. 4277
-
-
Werner, R.F.1
-
6
-
-
0035157443
-
-
PHYADX 0378-4371 10.1016/S0378-4371(00)00476-3
-
S. Abe and A. K. Rajagopal, Physica A PHYADX 0378-4371 10.1016/S0378-4371(00)00476-3 289, 157 (2001);
-
(2001)
Physica A
, vol.289
, pp. 157
-
-
Abe, S.1
Rajagopal, A.K.2
-
7
-
-
4244020670
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.63.042104
-
C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.042104 63, 042104 (2001);
-
(2001)
Phys. Rev. A
, vol.63
, pp. 042104
-
-
Tsallis, C.1
Lloyd, S.2
Baranger, M.3
-
8
-
-
0036148551
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.65.012101
-
K. Zyczkowski, P. Horodecki, M. Horodecki, and R. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.012101 65, 012101 (2001);
-
(2001)
Phys. Rev. A
, vol.65
, pp. 012101
-
-
Zyczkowski, K.1
Horodecki, P.2
Horodecki, M.3
Horodecki, R.4
-
9
-
-
33344460737
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.71.024301
-
J. Batle, M. Casas, A. Plastino, and A. R. Plastino, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.024301 71, 024301 (2005), and references therein.
-
(2005)
Phys. Rev. A
, vol.71
, pp. 024301
-
-
Batle, J.1
Casas, M.2
Plastino, A.3
Plastino, A.R.4
-
11
-
-
6144253009
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.79.5194
-
N. J. Cerf and C. Adami, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.5194 79, 5194 (1997).
-
(1997)
Phys. Rev. Lett.
, vol.79
, pp. 5194
-
-
Cerf, N.J.1
Adami, C.2
-
12
-
-
38749101217
-
-
arXiv:quant-ph/0612050.
-
I. Devetak and J. Yard, e-print arXiv:quant-ph/0612050.
-
-
-
Devetak, I.1
Yard, J.2
-
13
-
-
38749112441
-
-
Ph.D. thesis, Swiss Federal Institute of Technology
-
R. Renner, Ph.D. thesis, Swiss Federal Institute of Technology, 2005;
-
(2005)
-
-
Renner, R.1
-
16
-
-
14344280570
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.60.893
-
N. J. Cerf and C. Adami, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.893 60, 893 (1999).
-
(1999)
Phys. Rev. A
, vol.60
, pp. 893
-
-
Cerf, N.J.1
Adami, C.2
-
17
-
-
0001339646
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.54.1838
-
R. Horodecki and M. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.1838 54, 1838 (1996).
-
(1996)
Phys. Rev. A
, vol.54
, pp. 1838
-
-
Horodecki, R.1
Horodecki, M.2
-
18
-
-
0037174198
-
-
TCSCDI 0304-3975 10.1016/S0304-3975(02)00139-1
-
B. M. Terhal, Theor. Comput. Sci. TCSCDI 0304-3975 10.1016/S0304-3975(02) 00139-1 287, 313 (2002).
-
(2002)
Theor. Comput. Sci.
, vol.287
, pp. 313
-
-
Terhal, B.M.1
-
19
-
-
0035981730
-
-
JMAPAQ 0022-2488 10.1063/1.1498490
-
K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1498490 43, 4299 (2002).
-
(2002)
J. Math. Phys.
, vol.43
, pp. 4299
-
-
Vollbrecht, K.G.H.1
Wolf, M.M.2
-
20
-
-
0037965689
-
-
See Ref. and references therein. For discrete variables see in particular PLRAAN 1050-2947 10.1103/PhysRevA.67.022320
-
See Ref. and references therein. For discrete variables see in particular V. Giovannetti, S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.022320 67, 022320 (2003);
-
(2003)
Phys. Rev. A
, vol.67
, pp. 022320
-
-
Giovannetti, V.1
Mancini, S.2
Vitali, D.3
Tombesi, P.4
-
21
-
-
0242694950
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.68.032103
-
H. F. Hofmann and S. Takeuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032103 68, 032103 (2003);
-
(2003)
Phys. Rev. A
, vol.68
, pp. 032103
-
-
Hofmann, H.F.1
Takeuchi, S.2
-
22
-
-
2342501807
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.92.117903
-
O. Gühne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 117903 92, 117903 (2004);
-
(2004)
Phys. Rev. Lett.
, vol.92
, pp. 117903
-
-
Gühne, O.1
-
23
-
-
27144489128
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.72.022340
-
G. Tóth and O. Gühne, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022340 72, 022340 (2005);
-
(2005)
Phys. Rev. A
, vol.72
, pp. 022340
-
-
Tóth, G.1
Gühne, O.2
-
25
-
-
33646347409
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.96.170502
-
O. Gühne and N. Lütkenhaus, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.170502 96, 170502 (2006);
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 170502
-
-
Gühne, O.1
Lütkenhaus, N.2
-
26
-
-
34848900128
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.99.130504
-
O. Gühne, P. Hyllus, O. Gittsovich, and J. Eisert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.130504 99, 130504 (2007);
-
(2007)
Phys. Rev. Lett.
, vol.99
, pp. 130504
-
-
Gühne, O.1
Hyllus, P.2
Gittsovich, O.3
Eisert, J.4
-
27
-
-
38749123062
-
-
arXiv:quant-ph/0612177.
-
F. A. Bovino, e-print arXiv:quant-ph/0612177.
-
-
-
Bovino, F.A.1
-
28
-
-
19544375232
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.70.022316
-
O. Gühne and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.022316 70, 022316 (2004).
-
(2004)
Phys. Rev. A
, vol.70
, pp. 022316
-
-
Gühne, O.1
Lewenstein, M.2
-
29
-
-
33244479165
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.95.240407
-
F. A. Bovino, G. Castagnoli, A. Ekert, P. Horodecki, C. M. Alves, and A. V. Sergienko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.240407 95, 240407 (2005).
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 240407
-
-
Bovino, F.A.1
Castagnoli, G.2
Ekert, A.3
Horodecki, P.4
Alves, C.M.5
Sergienko, A.V.6
-
30
-
-
0035804232
-
-
NATUAS 0028-0836 10.1038/35051038
-
A. Soerensen, L.-M. Duan, J. I. Cirac, and P. Zoller, Nature (London) NATUAS 0028-0836 10.1038/35051038 409, 63 (2001);
-
(2001)
Nature (London)
, vol.409
, pp. 63
-
-
Soerensen, A.1
Duan, L.-M.2
Cirac, J.I.3
Zoller, P.4
-
31
-
-
33750993044
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.74.052319
-
J. K. Korbicz, O. Gühne, M. Lenensten, H. Haffner, C. F. Roos, and R. Blatt, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.052319 74, 052319 (2006);
-
(2006)
Phys. Rev. A
, vol.74
, pp. 052319
-
-
Korbicz, J.K.1
Gühne, O.2
Lenensten, M.3
Haffner, H.4
Roos, C.F.5
Blatt, R.6
-
32
-
-
33646168800
-
-
NATUAS 0028-0836 10.1038/nature04627
-
S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich, F. Mintert, and A. Buchleitner, Nature (London) NATUAS 0028-0836 10.1038/nature04627 440, 1022 (2006).
-
(2006)
Nature (London)
, vol.440
, pp. 1022
-
-
Walborn, S.P.1
Souto Ribeiro, P.H.2
Davidovich, L.3
Mintert, F.4
Buchleitner, A.5
-
33
-
-
0037574296
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413
-
A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
-
(1996)
Phys. Rev. Lett.
, vol.77
, pp. 1413
-
-
Peres, A.1
-
35
-
-
4043133089
-
-
OSIDFU 1230-1612 10.1023/A:1025123923519
-
A. Kossakowski, Open Syst. Inf. Dyn. OSIDFU 1230-1612 10.1023/A:1025123923519 10, 221 (2003);
-
(2003)
Open Syst. Inf. Dyn.
, vol.10
, pp. 221
-
-
Kossakowski, A.1
-
36
-
-
21244500035
-
-
OSIDFU 1230-1612 10.1007/s11080-004-6625-3
-
G. Kimura and A. Kossakowski, Open Syst. Inf. Dyn. OSIDFU 1230-1612 10.1007/s11080-004-6625-3 11, 343 (2004).
-
(2004)
Open Syst. Inf. Dyn.
, vol.11
, pp. 343
-
-
Kimura, G.1
Kossakowski, A.2
-
37
-
-
0000592520
-
-
PYLAAG 0375-9601 10.1016/S0375-9601(00)00401-1
-
B. M. Terhal, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00401- 1 271, 319 (2000).
-
(2000)
Phys. Lett. A
, vol.271
, pp. 319
-
-
Terhal, B.M.1
-
38
-
-
0035584893
-
-
LAAPAW 0024-3795 10.1016/S0024-3795(00)00251-2
-
B. M. Terhal, Linear Algebr. Appl. LAAPAW 0024-3795 10.1016/S0024- 3795(00)00251-2 323, 61 (2001).
-
(2001)
Linear Algebr. Appl.
, vol.323
, pp. 61
-
-
Terhal, B.M.1
-
39
-
-
0037120391
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.89.127902
-
P. Horodecki and A. Ekert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.127902 89, 127902 (2002);
-
(2002)
Phys. Rev. Lett.
, vol.89
, pp. 127902
-
-
Horodecki, P.1
Ekert, A.2
-
40
-
-
85038282356
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.90.167901
-
P. Horodecki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90. 167901 90, 167901 (2003);
-
(2003)
Phys. Rev. Lett.
, vol.90
, pp. 167901
-
-
Horodecki, P.1
-
41
-
-
0242694957
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.68.032306
-
C. Moura Alves, P. Horodecki, D. K. L. Oi, L. C. Kwek, and A. K. Ekert, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032306 68, 032306 (2003);
-
(2003)
Phys. Rev. A
, vol.68
, pp. 032306
-
-
Moura Alves, C.1
Horodecki, P.2
Oi, D.K.L.3
Kwek, L.C.4
Ekert, A.K.5
-
42
-
-
18044371044
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.94.040502
-
H. A. Carteret, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94. 040502 94, 040502 (2005).
-
(2005)
Phys. Rev. Lett.
, vol.94
, pp. 040502
-
-
Carteret, H.A.1
-
44
-
-
18344374018
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.60.898
-
N. J. Cerf, C. Adami, and R. M. Gingrich, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.898 60, 898 (1999).
-
(1999)
Phys. Rev. A
, vol.60
, pp. 898
-
-
Cerf, N.J.1
Adami, C.2
Gingrich, R.M.3
-
45
-
-
0000525266
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.59.4206
-
M. Horodecki and P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.4206 59, 4206 (1999).
-
(1999)
Phys. Rev. A
, vol.59
, pp. 4206
-
-
Horodecki, M.1
Horodecki, P.2
-
46
-
-
0942278545
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.68.052101
-
P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.052101 68, 052101 (2003).
-
(2003)
Phys. Rev. A
, vol.68
, pp. 052101
-
-
Horodecki, P.1
-
47
-
-
33747779703
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.97.080501
-
H.-P. Breuer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97. 080501 97, 080501 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.97
, pp. 080501
-
-
Breuer, H.-P.1
-
48
-
-
33748553326
-
-
JPHAC5 0305-4470 10.1088/0305-4470/39/38/010
-
H.-P. Breuer, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/38/010 39, 11847 (2006).
-
(2006)
J. Phys. A
, vol.39
, pp. 11847
-
-
Breuer, H.-P.1
-
49
-
-
34249731033
-
-
JPHAC5 0305-4470 10.1088/1751-8113/40/23/012
-
W. Hall, J. Phys. A JPHAC5 0305-4470 10.1088/1751-8113/40/23/012 40, 6183 (2007).
-
(2007)
J. Phys. A
, vol.40
, pp. 6183
-
-
Hall, W.1
-
51
-
-
38749142420
-
-
note
-
This could be proved using the fact that positive matrices are always Hermitian and have positive eigenvalues. Then the spectral decompositions A= i λiA iA i and B= i λiB iB iB lead to TrAB= i,j λiA λjB ijB 2 ≥0.
-
-
-
-
52
-
-
0001339646
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.54.1838
-
R. Horodecki and M. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.1838 54, 1838 (1996).
-
(1996)
Phys. Rev. A
, vol.54
, pp. 1838
-
-
Horodecki, R.1
Horodecki, M.2
-
53
-
-
0033701916
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.61.062312
-
D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and A. V. Thapliyal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.062312 61, 062312 (2000).
-
(2000)
Phys. Rev. A
, vol.61
, pp. 062312
-
-
Divincenzo, D.P.1
Shor, P.W.2
Smolin, J.A.3
Terhal, B.M.4
Thapliyal, A.V.5
-
54
-
-
38749108713
-
-
note
-
We assume here α to be natural number since in the case of entangled the operator + τ A (B) U () may not be positive.
-
-
-
-
55
-
-
0000525266
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.59.4206
-
M. Horodecki and P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.4206 59, 4206 (1999).
-
(1999)
Phys. Rev. A
, vol.59
, pp. 4206
-
-
Horodecki, M.1
Horodecki, P.2
-
58
-
-
0141684697
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.68.012309
-
J. Schliemann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.012309 68, 012309 (2003);
-
(2003)
Phys. Rev. A
, vol.68
, pp. 012309
-
-
Schliemann, J.1
-
59
-
-
27144550742
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.72.012307
-
J. Schliemann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.012307 72, 012307 (2005);
-
(2005)
Phys. Rev. A
, vol.72
, pp. 012307
-
-
Schliemann, J.1
-
60
-
-
26944486805
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.71.062330
-
H.-P. Breuer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.062330 71, 062330 (2005);
-
(2005)
Phys. Rev. A
, vol.71
, pp. 062330
-
-
Breuer, H.-P.1
-
61
-
-
25844515791
-
-
JPHAC5 0305-4470 10.1088/0305-4470/38/41/013
-
H.-P. Breuer, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/41/013 38, 9019 (2005);
-
(2005)
J. Phys. A
, vol.38
, pp. 9019
-
-
Breuer, H.-P.1
-
63
-
-
33846669597
-
-
PYLAAG 0375-9601 10.1016/j.physleta.2006.11.036
-
R. Augusiak and J. Stasińska, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2006.11.036 363, 182 (2007).
-
(2007)
Phys. Lett. A
, vol.363
, pp. 182
-
-
Augusiak, R.1
Stasińska, J.2
-
64
-
-
34147126932
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.98.140505
-
F. Mintert and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.140505 98, 140505 (2007);
-
(2007)
Phys. Rev. Lett.
, vol.98
, pp. 140505
-
-
Mintert, F.1
Buchleitner, A.2
-
65
-
-
34247891568
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.75.052302
-
F. Mintert, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.052302 75, 052302 (2007).
-
(2007)
Phys. Rev. A
, vol.75
, pp. 052302
-
-
Mintert, F.1
-
67
-
-
38749143156
-
-
In fact the ordering is not required and is put here only for convinience.
-
In fact the ordering is not required and is put here only for convinience.
-
-
-
-
68
-
-
13444276016
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.93.110501
-
C. Moura Alves and D. Jaksch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.110501 93, 110501 (2004).
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 110501
-
-
Moura Alves, C.1
Jaksch, D.2
-
69
-
-
30344481393
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.95.260502
-
F. Mintert, M. Kuś, and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.260502 95, 260502 (2005).
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 260502
-
-
Mintert, F.1
Kuś, M.2
Buchleitner, A.3
-
70
-
-
27144446447
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.72.012337
-
A. Osterloh and J. Siewert, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.012337 72, 012337 (2005).
-
(2005)
Phys. Rev. A
, vol.72
, pp. 012337
-
-
Osterloh, A.1
Siewert, J.2
|