-
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
-
-
0000486090
-
-
0148-6349
-
J. S. Bell, Physics 1, 195 (1964). 0148-6349
-
(1964)
Physics
, vol.1
, pp. 195
-
-
Bell, J.S.1
-
4
-
-
34547380185
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.98.230501
-
A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.230501 98, 230501 (2007).
-
(2007)
Phys. Rev. Lett.
, vol.98
, pp. 230501
-
-
Acín, A.1
Brunner, N.2
Gisin, N.3
Massar, S.4
Pironio, S.5
Scarani, V.6
-
5
-
-
0003056889
-
-
PYLAAG 0375-9601 10.1016/0375-9601(92)90952-I
-
A. Elitzur, S. Popescu, and D. Rohrlich, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90952-I 162, 25 (1992).
-
(1992)
Phys. Lett. A
, vol.162
, pp. 25
-
-
Elitzur, A.1
Popescu, S.2
Rohrlich, D.3
-
6
-
-
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
-
7
-
-
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
-
9
-
-
40849120793
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.100.090403
-
L. Masanes, Y. C. Liang, and A. C. Doherty, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.090403 100, 090403 (2008).
-
(2008)
Phys. Rev. Lett.
, vol.100
, pp. 090403
-
-
Masanes, L.1
Liang, Y.C.2
Doherty, A.C.3
-
10
-
-
42449154884
-
-
Indeed, one can always see a measurement as consisting of two steps: (i) projection on a basis, and (ii) attribution of a numerical value for the outcome associated to each element of the basis. This numerical value is purely a label: any choice is valid, provided it does not erase information, as it would be the case if the same value would be associated to more than one outcome. For instance, one can choose RA = { 1,2,..., dA } and RB = { 1,2,..., dB }.
-
Indeed, one can always see a measurement as consisting of two steps: (i) projection on a basis, and (ii) attribution of a numerical value for the outcome associated to each element of the basis. This numerical value is purely a label: any choice is valid, provided it does not erase information, as it would be the case if the same value would be associated to more than one outcome. For instance, one can choose RA = { 1,2,..., dA } and RB = { 1,2,..., dB }.
-
-
-
-
11
-
-
42449104623
-
-
Note also that, if ρ is pure, PL and PNL cannot be obtained from the measurement of a quantum state with the same dimensionality, otherwise one would be able to decompose a pure state as a convex combination of other states.
-
Note also that, if ρ is pure, PL and PNL cannot be obtained from the measurement of a quantum state with the same dimensionality, otherwise one would be able to decompose a pure state as a convex combination of other states.
-
-
-
-
12
-
-
0001658724
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.83.1874
-
G. Brassard, R. Cleve, and A. Tapp, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1874 83, 1874 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.83
, pp. 1874
-
-
Brassard, G.1
Cleve, R.2
Tapp, A.3
-
13
-
-
1142303557
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.91.187904
-
B. F. Toner and D. Bacon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.187904 91, 187904 (2003).
-
(2003)
Phys. Rev. Lett.
, vol.91
, pp. 187904
-
-
Toner, B.F.1
Bacon, D.2
-
14
-
-
21244476427
-
-
NJOPFM 1367-2630 10.1088/1367-2630/7/1/088
-
N. Brunner, N. Gisin, and V. Scarani, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/088 7, 88 (2005).
-
(2005)
New J. Phys.
, vol.7
, pp. 88
-
-
Brunner, N.1
Gisin, N.2
Scarani, V.3
-
15
-
-
27744461984
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.94.220403
-
N. J. Cerf, N. Gisin, S. Massar, and S. Popescu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.220403 94, 220403 (2005).
-
(2005)
Phys. Rev. Lett.
, vol.94
, pp. 220403
-
-
Cerf, N.J.1
Gisin, N.2
Massar, S.3
Popescu, S.4
-
16
-
-
33244477414
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.72.062314
-
J. Degorre, S. Laplante, and J. Roland, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.062314 72, 062314 (2005)
-
(2005)
Phys. Rev. A
, vol.72
, pp. 062314
-
-
Degorre, J.1
Laplante, S.2
Roland, J.3
-
17
-
-
33846401021
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.75.012309
-
J. Degorre, S. Laplante, and J. Roland, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.012309 75, 012309 (2007).
-
(2007)
Phys. Rev. A
, vol.75
, pp. 012309
-
-
Degorre, J.1
Laplante, S.2
Roland, J.3
-
18
-
-
33750486525
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.97.170409
-
J. Barrett, A. Kent, and S. Pironio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.170409 97, 170409 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.97
, pp. 170409
-
-
Barrett, J.1
Kent, A.2
Pironio, S.3
-
19
-
-
0000731967
-
-
PYLAAG 0375-9601 10.1016/0375-9601(91)90805-I
-
N. Gisin, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(91)90805-I 154, 201 (1991).
-
(1991)
Phys. Lett. A
, vol.154
, pp. 201
-
-
Gisin, N.1
-
20
-
-
0002315653
-
-
PYLAAG 0375-9601 10.1016/0375-9601(92)90949-M
-
N. Gisin and A. Peres, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90949-M 162, 15 (1992).
-
(1992)
Phys. Lett. A
, vol.162
, pp. 15
-
-
Gisin, N.1
Peres, A.2
-
21
-
-
0000365583
-
-
PYLAAG 0375-9601 10.1016/0375-9601(92)90711-T
-
S. Popescu and D. Rohrlich, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90711-T 166, 293 (1992).
-
(1992)
Phys. Lett. A
, vol.166
, pp. 293
-
-
Popescu, S.1
Rohrlich, D.2
-
22
-
-
0038540448
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.90.157903
-
B. M. Terhal, A. C. Doherty, and D. Schwab, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.157903 90, 157903 (2003).
-
(2003)
Phys. Rev. Lett.
, vol.90
, pp. 157903
-
-
Terhal, B.M.1
Doherty, A.C.2
Schwab, D.3
-
23
-
-
34547416463
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.99.040403
-
M. L. Almeida, S. Pironio, J. Barrett, G. Tóth, and A. Acín, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.040403 99, 040403 (2007).
-
(2007)
Phys. Rev. Lett.
, vol.99
, pp. 040403
-
-
Almeida, M.L.1
Pironio, S.2
Barrett, J.3
Tóth, G.4
Acín, A.5
-
24
-
-
0036542261
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.65.042302
-
J. Barrett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.042302 65, 042302 (2002).
-
(2002)
Phys. Rev. A
, vol.65
, pp. 042302
-
-
Barrett, J.1
-
25
-
-
26944471711
-
-
In the multipartite case, pL max (ρ) =0 holds for all states that exhibit a Greenberger-Horne-Zeilinger-type of nonlocality. There are examples of such states that are not maximally entangled and actually mixed PLRAAN 1050-2947 10.1103/PhysRevA.71.042325
-
In the multipartite case, pL max (ρ) =0 holds for all states that exhibit a Greenberger-Horne-Zeilinger-type of nonlocality. There are examples of such states that are not maximally entangled and actually mixed [V. Scarani, A. Acín, E. Schenck, and M. Aspelmeyer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.042325 71, 042325 (2005)]. Note that, for a N -partite state, pL max (ρ) =0 does not necessarily imply genuine N -party nonlocality.
-
(2005)
Phys. Rev. A
, vol.71
, pp. 042325
-
-
Scarani, V.1
Acín, A.2
Schenck, E.3
Aspelmeyer, M.4
-
26
-
-
21344488159
-
-
FNDPA4 0015-9018 10.1007/BF02058098
-
S. Popescu and D. Rohrlich, Found. Phys. FNDPA4 0015-9018 10.1007/BF02058098 24, 379 (1994).
-
(1994)
Found. Phys.
, vol.24
, pp. 379
-
-
Popescu, S.1
Rohrlich, D.2
-
27
-
-
42449129921
-
-
The elegant proof that follows is due to Cyril Branciard and reproduced with his permission.
-
The elegant proof that follows is due to Cyril Branciard and reproduced with his permission.
-
-
-
-
28
-
-
36049056258
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.23.880
-
J. F. Clauser, M. A. Horne, A. Shimony, and R. A. 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.A.4
-
29
-
-
34250250611
-
-
LMPHDY 0377-9017 10.1007/BF00417500
-
B. S. Cirel'son, Lett. Math. Phys. LMPHDY 0377-9017 10.1007/BF00417500 4, 93 (1980).
-
(1980)
Lett. Math. Phys.
, vol.4
, pp. 93
-
-
Cirel'Son, B.S.1
-
30
-
-
42449153542
-
-
Note that the band defined by | az |, | bz | ≤ 1-s c becomes narrower when approaching the maximally entangled state. From this perspective, the decomposition we have just found behaves in a discontinuous way: (i) for the maximally entangled state, PNL = PQ has random marginals and correlations defined by a scalar product; and (ii) for highly but nonmaximally entangled states (θ= π 4 -ε), such a simple form is, however, retained only for a narrow band of settings; the band increases when going to weakly entangled states, filling ultimately again the whole sphere for θ=0, in which case, however, the weight of PNL is zero.
-
Note that the band defined by | az |, | bz | ≤ 1-s c becomes narrower when approaching the maximally entangled state. From this perspective, the decomposition we have just found behaves in a discontinuous way: (i) for the maximally entangled state, PNL = PQ has random marginals and correlations defined by a scalar product; and (ii) for highly but nonmaximally entangled states (θ= π 4 -ε), such a simple form is, however, retained only for a narrow band of settings; the band increases when going to weakly entangled states, filling ultimately again the whole sphere for θ=0, in which case, however, the weight of PNL is zero.
-
-
-
-
32
-
-
33746933894
-
-
PRVDAQ 0556-2821 10.1103/PhysRevD.2.1418
-
P. A. Pearle, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.2.1418 2, 1418 (1970).
-
(1970)
Phys. Rev. D
, vol.2
, pp. 1418
-
-
Pearle, P.A.1
-
33
-
-
0036577393
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.65.052325
-
A. Acín, T. Durt, N. Gisin, and J. I. Latorre, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.052325 65, 052325 (2002).
-
(2002)
Phys. Rev. A
, vol.65
, pp. 052325
-
-
Acín, A.1
Durt, T.2
Gisin, N.3
Latorre, J.I.4
-
34
-
-
28844435660
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.95.210402
-
A. Acín, R. Gill, and N. Gisin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.210402 95, 210402 (2005).
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 210402
-
-
Acín, A.1
Gill, R.2
Gisin, N.3
-
35
-
-
33750439445
-
-
PLRAAN 1050-2947 10.1103/PhysRevA.74.042339
-
V. Scarani, N. Gisin, N. Brunner, L. Masanes, S. Pino, and A. Acín, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.042339 74, 042339 (2006).
-
(2006)
Phys. Rev. A
, vol.74
, pp. 042339
-
-
Scarani, V.1
Gisin, N.2
Brunner, N.3
Masanes, L.4
Pino, S.5
Acín, A.6
-
36
-
-
42449130770
-
-
For the whole region 0<γ<1, the upper bound 6 obtained using the chained inequality gives a strictly positive number
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For the whole region 0<γ<1, the upper bound 6 obtained using the chained inequality gives a strictly positive number [S. Pironio (private communication)].
-
-
-
Pironio, S.1
-
37
-
-
42449110582
-
-
It is an interesting open question, whether pL max (ρ) <1 implies the possibility of checking nonlocality with a finite number of settings.
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It is an interesting open question, whether pL max (ρ) <1 implies the possibility of checking nonlocality with a finite number of settings.
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