-
3
-
-
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
-
5
-
-
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
-
-
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
-
7
-
-
0035679286
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.64.062307
-
K. G. H. Vollbrecht and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.062307 64, 062307 (2001).
-
(2001)
Phys. Rev. A
, vol.64
, pp. 062307
-
-
Vollbrecht, K.G.H.1
Werner, R.F.2
-
8
-
-
18344383219
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.63.042111
-
T. Eggeling and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.042111 63, 042111 (2001).
-
(2001)
Phys. Rev. A
, vol.63
, pp. 042111
-
-
Eggeling, T.1
Werner, R.F.2
-
9
-
-
0000620953
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.83.436
-
M. A. Nielsen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83. 436 83, 436 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.83
, pp. 436
-
-
Nielsen, M.A.1
-
10
-
-
0034652055
-
-
JMOPEW 0950-0340 10.1080/095003400148268
-
G. Vidal, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003400148268 47, 355 (2000).
-
(2000)
J. Mod. Opt.
, vol.47
, pp. 355
-
-
Vidal, G.1
-
11
-
-
0000953494
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.62.062314
-
W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.062314 62, 062314 (2000).
-
(2000)
Phys. Rev. A
, vol.62
, pp. 062314
-
-
Dür, W.1
Vidal, G.2
Cirac, J.I.3
-
12
-
-
0000303412
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.83.1046
-
G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1046 83, 1046 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.83
, pp. 1046
-
-
Vidal, G.1
-
13
-
-
4243445702
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.53.2046
-
C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.53.2046 53, 2046 (1996).
-
(1996)
Phys. Rev. A
, vol.53
, pp. 2046
-
-
Bennett, C.H.1
Bernstein, H.J.2
Popescu, S.3
Schumacher, B.4
-
14
-
-
4143072819
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.83.2656
-
A. Kent, N. Linden, and S. Massar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.2656 83, 2656 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.83
, pp. 2656
-
-
Kent, A.1
Linden, N.2
Massar, S.3
-
15
-
-
0034706481
-
-
PYLAAG 0375-9601 10.1016/S0375-9601(00)00611-3
-
L.-X. Cen, F.-L. Li, and S.-Y. Zhu, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00611-3 275, 368 (2000)
-
(2000)
Phys. Lett. A
, vol.275
, pp. 368
-
-
Cen, L.-X.1
Li, F.-L.2
Zhu, S.-Y.3
-
16
-
-
0036577433
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.65.052318
-
L.-X. Cen, N.-J. Wu, F.-H. Yang, and J.-H. An, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.052318 65, 052318 (2002).
-
(2002)
Phys. Rev. A
, vol.65
, pp. 052318
-
-
Cen, L.-X.1
Wu, N.-J.2
Yang, F.-H.3
An, J.-H.4
-
17
-
-
4644359625
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.78.5022
-
S. Hill and W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.5022 78, 5022 (1997).
-
(1997)
Phys. Rev. Lett.
, vol.78
, pp. 5022
-
-
Hill, S.1
Wootters, W.K.2
-
18
-
-
0035396243
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.64.010101
-
F. Verstraete, J. Dehaene, and B. DeMoor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.010101 64, 010101 (R) (2001).
-
(2001)
Phys. Rev. A
, vol.64
, pp. 010101
-
-
Verstraete, F.1
Dehaene, J.2
Demoor, B.3
-
19
-
-
38549141303
-
-
Obviously, unique up to local unitary transformations.
-
Obviously, unique up to local unitary transformations.
-
-
-
-
20
-
-
38549182559
-
-
Maximal, in the sense that no SLOCC transformations can bring the state to another one with higher entanglement of formation.
-
Maximal, in the sense that no SLOCC transformations can bring the state to another one with higher entanglement of formation.
-
-
-
-
21
-
-
0036508820
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.65.032308
-
F. Verstraete, J. Dehaene, and B. DeMoor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032308 65, 032308 (2002).
-
(2002)
Phys. Rev. A
, vol.65
, pp. 032308
-
-
Verstraete, F.1
Dehaene, J.2
Demoor, B.3
-
23
-
-
4243656245
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.74.2619
-
S. Popescu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.2619 74, 2619 (1995)
-
(1995)
Phys. Rev. Lett.
, vol.74
, pp. 2619
-
-
Popescu, S.1
-
24
-
-
0000296001
-
-
PYLAAG 0375-9601 10.1016/S0375-9601(96)80001-6
-
N. Gisin, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)80001-6 210, 151 (1996).
-
(1996)
Phys. Lett. A
, vol.210
, pp. 151
-
-
Gisin, N.1
-
25
-
-
36049056258
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.23.880
-
J. F. Clauser, M. A. Horne, A. Shimony, and R. Holt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.23.880 23, 880 (1969)
-
(1969)
Phys. Rev. Lett.
, vol.23
, pp. 880
-
-
Clauser, J.F.1
Horne, M.A.2
Shimony, A.3
Holt, R.4
-
27
-
-
38549129901
-
-
Their separability can be veirfied, for example, by writing these operators in full in the product basis via Eq. 4 and showing that they admit convex decomposition in terms of separable states. Alternatively, via the Choi-Jamiołkowski isomorphism that will be discussed later in Sec. 3 and the remarks made towards the end of Sec. 3, one can also see that these matrices correspond to separable states.
-
Their separability can be veirfied, for example, by writing these operators in full in the product basis via Eq. 4 and showing that they admit convex decomposition in terms of separable states. Alternatively, via the Choi-Jamiołkowski isomorphism that will be discussed later in Sec. 3 and the remarks made towards the end of Sec. 3, one can also see that these matrices correspond to separable states.
-
-
-
-
29
-
-
38549180705
-
-
This software package, which stands for POlyhedron Representation Transformation Algorithm, is available at
-
This software package, which stands for POlyhedron Representation Transformation Algorithm, is available at http://www.zib.de/Optimization/ Software/Porta/
-
-
-
-
32
-
-
0030106462
-
-
SIREAD 0036-1445 10.1137/1038003
-
L. Vandenberghe and S. Boyd, SIAM Rev. SIREAD 0036-1445 10.1137/1038003 38, 49 (1996)
-
(1996)
SIAM Rev.
, vol.38
, pp. 49
-
-
Vandenberghe, L.1
Boyd, S.2
-
34
-
-
38549084308
-
-
http://www.physics.uq.edu.au/qisci/yerng/
-
-
-
-
35
-
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38549114192
-
-
Note that to verify Z2 against Eq. 9, one should also rewrite Zw,2 obtained in Eq. 8 in the appropriate tensor-product basis such that Zw,2 acts on H A′ H A″ H B′ H B″.
-
Note that to verify Z2 against Eq. 9, one should also rewrite Zw,2 obtained in Eq. 8 in the appropriate tensor-product basis such that Zw,2 acts on H A′ H A″ H B′ H B″.
-
-
-
-
36
-
-
35448975107
-
-
RMHPBE 0034-4877 10.1016/0034-4877(72)90011-0
-
A. Jamiołkowski, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(72)90011-0 3, 275 (1972)
-
(1972)
Rep. Math. Phys.
, vol.3
, pp. 275
-
-
Jamiołkowski, A.1
-
37
-
-
0016522050
-
-
LAAPAW 0024-3795 10.1016/0024-3795(75)90075-0
-
M. D. Choi, Linear Algebr. Appl. LAAPAW 0024-3795 10.1016/0024-3795(75) 90075-0 10, 285 (1975)
-
(1975)
Linear Algebr. Appl.
, vol.10
, pp. 285
-
-
Choi, M.D.1
-
38
-
-
0008689297
-
-
RMHPBE 0034-4877 10.1016/0034-4877(86)90039-X
-
V. P. Belavkin and P. Staszewski, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(86)90039-X 24, 49 (1986).
-
(1986)
Rep. Math. Phys.
, vol.24
, pp. 49
-
-
Belavkin, V.P.1
Staszewski, P.2
-
39
-
-
38549136967
-
-
arXiv:quant-ph/9707002.
-
E. M. Rains, e-print arXiv:quant-ph/9707002.
-
-
-
Rains, E.M.1
-
40
-
-
0032025985
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.57.1619
-
V. Vedral and M. B. Plenio, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.1619 57, 1619 (1998).
-
(1998)
Phys. Rev. A
, vol.57
, pp. 1619
-
-
Vedral, V.1
Plenio, M.B.2
-
41
-
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38549110746
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Following Kraus' work on CPM, this specific form of the CPM is also known as a Kraus decomposition of the CPM, with each Ai Bi in the sum conventionally called the Kraus operator associated with the CPM.
-
Following Kraus' work on CPM, this specific form of the CPM is also known as a Kraus decomposition of the CPM, with each Ai Bi in the sum conventionally called the Kraus operator associated with the CPM.
-
-
-
-
43
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0003007332
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-
APNYA6 0003-4916 10.1016/0003-4916(71)90108-4
-
K. Kraus, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(71)90108-4 64, 311 (1971).
-
(1971)
Ann. Phys. (N.Y.)
, vol.64
, pp. 311
-
-
Kraus, K.1
-
44
-
-
0000795422
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.59.1070
-
C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.1070 59, 1070 (1999).
-
(1999)
Phys. Rev. A
, vol.59
, pp. 1070
-
-
Bennett, C.H.1
Divincenzo, D.P.2
Fuchs, C.A.3
Mor, T.4
Rains, E.5
Shor, P.W.6
Smolin, J.A.7
Wootters, W.K.8
-
45
-
-
0038721037
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.86.544
-
J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.544 86, 544 (2001).
-
(2001)
Phys. Rev. Lett.
, vol.86
, pp. 544
-
-
Cirac, J.I.1
Dür, W.2
Kraus, B.3
Lewenstein, M.4
-
46
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38549163380
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The ρE derived from G0 in Eq. 6 is an example of this sort. In fact, in this case, if the input state has no support on Π1 nor Π2, the map always outputs the zero matrix.
-
The ρE derived from G0 in Eq. 6 is an example of this sort. In fact, in this case, if the input state has no support on Π1 nor Π2, the map always outputs the zero matrix.
-
-
-
-
47
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38549102739
-
-
Since the mapping from any ρ Ps to a separable CPM via Eq. 13 is only defined up to a positive constant, for the subsequent discussion, we might as well consider the cone generated by Ps.
-
Since the mapping from any ρ Ps to a separable CPM via Eq. 13 is only defined up to a positive constant, for the subsequent discussion, we might as well consider the cone generated by Ps.
-
-
-
-
49
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38549098713
-
-
Strictly, the inequality 23 is only valid when λ3 λ4. When λ3 = λ4, F2 degenerates into an edge of the polytope Pλ. If λ1 = λ2, F2 collapses into a single point λ= λ 12 = λ (34).
-
Strictly, the inequality 23 is only valid when λ3 λ4. When λ3 = λ4, F2 degenerates into an edge of the polytope Pλ. If λ1 = λ2, F2 collapses into a single point λ = λ 12 = λ (34).
-
-
-
-
50
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-
38549111527
-
-
Within TE, 1-2 λ2 -2 λ3 =0 only when λ = λ 12 and λ (23) = λ 13. In this case, F3 degenerates into the line joining λ 12 and λ 13.
-
Within TE, 1-2 λ2 -2 λ3 =0 only when λ = λ 12 and λ (23) = λ 13. In this case, F3 degenerates into the line joining λ 12 and λ 13.
-
-
-
-
51
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38549148924
-
-
By this, of course, we are referring only to the states given in Eq. 31 that are originally of rank 3, and which becomes rank 2 upon quasidistillation. The states given in Eq. 31 that are of rank 2 get quasidistilled to the singlet state and so the process is clearly reversible in this case.
-
By this, of course, we are referring only to the states given in Eq. 31 that are originally of rank 3, and which becomes rank 2 upon quasidistillation. The states given in Eq. 31 that are of rank 2 get quasidistilled to the singlet state and so the process is clearly reversible in this case.
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