-
1
-
-
0000986501
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.59.141
-
G. Vidal and R. Tarrach, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.141 59, 141 (1999).
-
(1999)
Phys. Rev. A
, vol.59
, pp. 141
-
-
Vidal, G.1
Tarrach, R.2
-
2
-
-
0035963009
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.86.5184
-
M. A. Nielsen and J. Kempe, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5184 86, 5184 (2001).
-
(2001)
Phys. Rev. Lett.
, vol.86
, pp. 5184
-
-
Nielsen, M.A.1
Kempe, J.2
-
3
-
-
0141684701
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.68.012308
-
A. W. Harrow and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.012308 68, 012308 (2003).
-
(2003)
Phys. Rev. A
, vol.68
, pp. 012308
-
-
Harrow, A.W.1
Nielsen, M.A.2
-
4
-
-
33646372979
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.73.044302
-
D. Cavalcanti, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.044302 73, 044302 (2006).
-
(2006)
Phys. Rev. A
, vol.73
, pp. 044302
-
-
Cavalcanti, D.1
-
5
-
-
0034689077
-
-
PYLAAG 0375-9601 10.1016/S0375-9601(00)00108-0
-
J. F. Du, M. J. Shi, X. Y. Zhou, and R. D. Han, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00108-0 267, 244 (2000).
-
(2000)
Phys. Lett. A
, vol.267
, pp. 244
-
-
Du, J.F.1
Shi, M.J.2
Zhou, X.Y.3
Han, R.D.4
-
7
-
-
0037768761
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.67.054305
-
M. Steiner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.054305 67, 054305 (2003)
-
(2003)
Phys. Rev. A
, vol.67
, pp. 054305
-
-
Steiner, M.1
-
8
-
-
34848885413
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.76.030301
-
F. G. S. L. Brandao, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76. 030301 76, 030301 (R) (2007)
-
(2007)
Phys. Rev. A
, vol.76
, pp. 030301
-
-
Brandao, L.S.F.G.1
-
9
-
-
40949165609
-
-
arXiv:quant-ph/0612072;
-
L. Clarisse, e-print arXiv:quant-ph/0612072
-
-
-
Clarisse, L.1
-
12
-
-
33747836504
-
-
APPLAB 0003-6951 10.1063/1.2337535
-
D. Cavalcanti and M. O. T. Cunha, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2337535 89, 084102 (2006).
-
(2006)
Appl. Phys. Lett.
, vol.89
, pp. 084102
-
-
Cavalcanti, D.1
Cunha, M.O.T.2
-
13
-
-
4243962237
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.82.5385
-
C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.5385 82, 5385 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.82
, pp. 5385
-
-
Bennett, C.H.1
Divincenzo, D.P.2
Mor, T.3
Shor, P.W.4
Smolin, J.A.5
Terhal, B.M.6
-
14
-
-
45849155293
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.70.050101
-
R. Orús and R. Tarrach, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.050101 70, 050101 (R) (2004).
-
(2004)
Phys. Rev. A
, vol.70
, pp. 050101
-
-
Orús, R.1
Tarrach, R.2
-
15
-
-
0042542909
-
-
PYLAAG 0375-9601 10.1016/S0375-9601(97)00416-7
-
P. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(97)00416- 7 232, 333 (1997)
-
(1997)
Phys. Lett. A
, vol.232
, pp. 333
-
-
Horodecki, P.1
-
19
-
-
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
-
20
-
-
0036147915
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.65.012323
-
G. Vidal and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.012323 65, 012323 (2001).
-
(2001)
Phys. Rev. A
, vol.65
, pp. 012323
-
-
Vidal, G.1
Cirac, J.I.2
-
21
-
-
0035307066
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.63.044304
-
M. Lewenstein, B. Kraus, P. Horodecki, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.044304 63, 044304 (2001).
-
(2001)
Phys. Rev. A
, vol.63
, pp. 044304
-
-
Lewenstein, M.1
Kraus, B.2
Horodecki, P.3
Cirac, J.I.4
-
22
-
-
0141782139
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.62.052310
-
M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.052310 62, 052310 (2000).
-
(2000)
Phys. Rev. A
, vol.62
, pp. 052310
-
-
Lewenstein, M.1
Kraus, B.2
Cirac, J.I.3
Horodecki, P.4
-
24
-
-
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
-
25
-
-
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
-
26
-
-
40949120862
-
-
We have Tr (W) = d1 d2 Tr (W I d1 d2) 0, by condition (i). If Tr (W) =0, we then see that the hyperplane in B, orthogonal to the vector W, touches the compact and convex set S at its point I/ (d1 d2). Thus, I/ (d1 d2) turns out to be a point on the boundary of S, and hence, each open neighborhood of I/ (d1 d2) will always contain at least one inseparable state of AB, which is not true, whatever be the suitable metric we choose (see).
-
We have Tr (W) = d1 d2 Tr (W I d1 d2) 0, by condition (i). If Tr (W) =0, we then see that the hyperplane in B, orthogonal to the vector W, touches the compact and convex set S at its point I/ (d1 d2). Thus, I/ (d1 d2) turns out to be a point on the boundary of S, and hence, each open neighborhood of I/ (d1 d2) will always contain at least one inseparable state of AB, which is not true, whatever be the suitable metric we choose (see).
-
-
-
-
27
-
-
0038288033
-
-
JMOPEW 0950-0340 10.1080/09500340110105975
-
D. Bruß, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, J. Mod. Opt. JMOPEW 0950-0340 10.1080/ 09500340110105975 49, 1399 (2002)
-
(2002)
J. Mod. Opt.
, vol.49
, pp. 1399
-
-
Bruß, D.1
Cirac, J.I.2
Horodecki, P.3
Hulpke, F.4
Kraus, B.5
Lewenstein, M.6
Sanpera, A.7
-
28
-
-
1642264932
-
-
edited by G. Leuchs and T. Beth Wiley-VCH, Verlag GmbH and Co. KGaA, Weinheim
-
K. Ekert, O. Gühne, F. Hulpke, P. Hyllus, J. Korbicz, J. Mompart, D. Bruß, M. Lewenstein, and A. Sanpera, in Quantum Information Processing, edited by, G. Leuchs, and, T. Beth, (Wiley-VCH, Verlag GmbH and Co. KGaA, Weinheim 2003).
-
(2003)
Quantum Information Processing
-
-
Ekert, K.1
Gühne, O.2
Hulpke, F.3
Hyllus, P.4
Korbicz, J.5
Mompart, J.6
Bruß, D.7
Lewenstein, M.8
Sanpera, A.9
-
29
-
-
40949094699
-
-
The state σρ S is "nearest" to the state ρ (P-B) in the sense that the distance d (ρ,σ) of ρ from any element σ of S achieves its minimum at the point σρ.
-
The state σρ S is "nearest" to the state ρ (P-B) in the sense that the distance d (ρ,σ) of ρ from any element σ of S achieves its minimum at the point σρ.
-
-
-
-
30
-
-
0036994563
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.66.062311
-
L. Gurvits and H. Barnum, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.062311 66, 062311 (2002).
-
(2002)
Phys. Rev. A
, vol.66
, pp. 062311
-
-
Gurvits, L.1
Barnum, H.2
-
31
-
-
40949123055
-
-
Note that this is not true, in general, for an arbitrary element of S. For example, if |Ψ A Ψ| is an entangled state in D, then the (unnormalized) state ρ= |ψ A ψ| ψ B ψ | +η |Ψ Ψ| is always entangled for all η>0 (where we have assumed that d1 ≤ d2, and for |ψ A = i=1 d1 λi |i A, we have | ψ B = i=1 d1 λi |i B). This is because ρ TB (the partial transposition of ρ with respect to the subsystem B) is not positive semidefinite when η>0. Hence there does not exist λ>0 such that the ball B (|ψ A ψ| ψ B ψ |; λ) contains only separable states.
-
Note that this is not true, in general, for an arbitrary element of S. For example, if |Ψ A Ψ| is an entangled state in D, then the (unnormalized) state ρ= |ψ A ψ| ψ B ψ | +η |Ψ Ψ| is always entangled for all η>0 (where we have assumed that d1 ≤ d2, and for |ψ A = i=1 d1 λi |i A, we have | ψ B = i=1 d1 λi |i B). This is because ρ TB (the partial transposition of ρ with respect to the subsystem B) is not positive semidefinite when η>0. Hence there does not exist λ>0 such that the ball B (|ψ A ψ| ψ B ψ |; λ) contains only separable states.
-
-
-
-
32
-
-
0000727092
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.58.883
-
K. Oyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.883 58, 883 (1998).
-
(1998)
Phys. Rev. A
, vol.58
, pp. 883
-
-
Oyczkowski, K.1
Horodecki, P.2
Sanpera, A.3
Lewenstein, M.4
-
33
-
-
27144465234
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.72.022310
-
F. G. S. L. Brandão, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022310 72, 022310 (2005).
-
(2005)
Phys. Rev. A
, vol.72
, pp. 022310
-
-
Brandão, F.G.S.L.1
-
34
-
-
42749100177
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.93.220503
-
F. G. S. L. Brandão and R. O. Vianna, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.220503 93, 220503 (2004).
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 220503
-
-
Brandão, F.G.S.L.1
Vianna, R.O.2
-
35
-
-
37649027712
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.70.062317
-
J. Eisert, P. Hyllus, O. Gühne, and M. Curty, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.062317 70, 062317 (2004).
-
(2004)
Phys. Rev. A
, vol.70
, pp. 062317
-
-
Eisert, J.1
Hyllus, P.2
Gühne, O.3
Curty, M.4
-
36
-
-
18244422208
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.68.042312
-
L. Gurvits and H. Barnum, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.042312 68, 042312 (2003).
-
(2003)
Phys. Rev. A
, vol.68
, pp. 042312
-
-
Gurvits, L.1
Barnum, H.2
-
37
-
-
0001412842
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.83.1054
-
S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1054 83, 1054 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.83
, pp. 1054
-
-
Braunstein, S.L.1
Caves, C.M.2
Jozsa, R.3
Linden, N.4
Popescu, S.5
Schack, R.6
|